V ol.:(0123456789)
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Experiments in Fluids (2020) 61:146
https://doi.org/10.1007/s00348-020-02979-7
RESEARCH ARTICLE
T uf t deflec tion velocimetr y: asimple method toextrac t quantitativ e
flow field inf ormation
BenSteinfur th 1 · C.Cur a 1 · J.Gehring 1 · J. W eiss 1
Received: 10 F ebruar y 2020 / Revised: 12 May 2020 / Accept ed: 15 May 2020 / Published online: 6 June 2020
© The Author(s) 2020
Abstr ac t
A no v el method capable of assessing flow fields in a q uic k and relativ ely sim ple manner is introduced. In an extension t o t he
classical qualitativ e flo w visualization by means of co tton or pol ymer ic tuf ts, digital dat a processing is used to e xtract the
or ientation of t hese tufts. This inf or mation can be related to phy sical quantities, in particular to time- and space-dependent
v elocity signals. The capability of this method is demonstrated in tw o test scenarios. First, it is applied to g ain inf or mation on
the unsteady near -w all flow along a turbulent separation bubble. Second, the tw o-component v elocity field in the w ake of a
generic car model is measured, allo wing f or a quantification of the recirculation zone dimensions. V alidation measur ements
with con v entional techniq ues, e.g., par ticle image v elocimetry , unsteady pressure measurements and ho t wire anemometr y ,
are conducted throughout the study . These generall y suggest that the no vel appr oach pro vides a quic k and reasonabl y good
quantitativ e ov er view of the flo w configurations. Ho we ver , the measurement er ror ma y be substantial in flo w regions of lo w
v elocity or dominated b y high-frequency oscillations.
Graphic abstract
-0.5

0
0.5
1
x (mm)

50
100
150
y (mm)

0 -5 01 00 50 150
T uft Deflection V elocimetry
uU / (-)

∞
x (mm)

0 -5 01 00 50 150
Particle Image Ve locimetry
1 Introduction
For centuries, visualizing fluid flow phenomena has pla yed a
cr ucial role in unders t anding the underl ying ph ysical mec ha -
nisms. This is due to the f act that “[...] once a phenomenon
is visualized, a lar ge s tep has been taken to w ard understand-
ing it and to w ard sol ving the t heoretical and e xper imental
problems in v olv ed” (W erle 1973 ). For e xample, the visu -
alization e xper iments of Re ynolds (1883) and Mach (1887)
Electronic supplementar y material The online v ersion of t his
ar ticle ( https ://doi.org/10.1007/s0034 8-020-02979 -7 ) contains
supplementar y mater ial, which is a vailable to authorized users.
* Ben Steinfurt h
ben.steinfurt [email protected]
J. W eiss
julien.weiss@tu-ber lin.de
1 Chair ofA erodynamics, T echnisc he Univ ersit ät Berlin,
Berlin, Germany

Experiments in Fluids (2020) 61:146
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contr ibuted significantl y to the understanding of fundamen -
tal flow ph ysics while more recentl y , the disco very of coher -
ent structures was enabled b y flow visualization me thods
(Bro wn and R oshk o 1974 ).
As sugges ted b y Ristić ( 2007 ), flo w visualization methods
can be classified into sur f ace flo w and off-the sur face flo w
visualization, depending on the flow r egion t hat is anal yzed.
Sur face flo w visualization is pr imar ily used to obtain inf or -
mation regarding the boundary lay er state, e.g., t he transition
point, the local direction of w all shear stress and the lines of
separation and reattachment. Along with oil film visualiza -
tion, a qualitativ e anal ysis with sur f ace tuf ts is commonl y
per f or med. The model is hereb y equipped with thin fabric
tufts t hat are glued to its surface. The orient ation of indi -
vidual tufts is t hen go v er ned by the space-dependent v eloc -
ity field, and intuitiv e conclusions regarding the flo w field
can be dra wn. A shor t and incomple te list of applications
includes air plane wings and components, wind turbines,
road v ehicles and race cars (Andino et al. 2015 ; Eggles -
ton and Starc her 1990 ; Fisher et al. 1991 ; Steinfurt h et al.
2019 ). Off-the sur face flo w visualization techniq ues are used
to visualize c haracter istic flo w f eatures outside t he bound -
ar y la y er b y indicating streamlines. This can be achie v ed
b y using smoke or oil drople ts in air and dy e/ink in w ater .
Ho we ver , tuf ts ma y be emplo y ed in this scenar io as well
b y ar ranging t hem in a gr idwise manner, e.g., attached t o a
screen. For e xample, placing this screen at v ar ious positions
in the flow enabled in v estigations of the longitudinal v or tices
in the w ake of a N A CA 0012 wing (Mason and Marc hman
III 1971 ), semiwing models (McCor mick e t al. 1968 ), rec -
tangular wings and delt a wings (Bird and Rile y 1952 ).
Pre vious studies ha ve sho wn t hat there is a larg e band -
width of possible operation scenar ios f or the classical tuf t
visualization techniq ue—both in sur f ace and off-sur f ace
application. This is no doubt due to the intuitive function
pr inciple of the approach as the free ends of the tufts mimic
the major flo w characteristics. Qualitativ e statements about
the flow can then readil y be made since the tuf t deflection
is directl y linked to local v elocity vectors through the flo w
momentum.
The desire to e xtend this con v entional approach and g ain
quantitativ e inf or mation regarding v elocity fields is theref ore
natural. Suc h a dev elopment, from a qualitativ e to a quanti -
tative me thod, is by no means ne w as f or instance, par ticle
image v elocimetr y has e v olv ed from flo w visualizations wit h
smoke particles, benefited by adv ancing imaging and dat a
processing methods.
Thus, a f ew recent s tudies were aimed at g aining quan -
titative insight fr om images of tuft visualization. V ey e t al.
( 2014 ) anal yze the stall beha vior of full-scale wind turbines
using per -tuft statistics as the indicator of the local flow .
The y link the tuf t angular standard deviation to the local
turbulence le vel whic h allow s f or t he determination of
separation lines. Wieser e tal. apply a similar me t hodology
to a realistic car model (W ieser etal. 2015 ) and full-scale
road v ehicles (Wieser et al. 2016 ). Here, mean tuf t angles are
also used to per f or m line integ ral con v olution (LIC). Their
results sho w good agreement between the calculated surface
traces and oil film visualization as w ell as CFD simulations
(Wieser e t al. 2016 ). Swytink -Binnema and Johnson ( 2016 )
determine t he blade stall from captured videos of the tufts
applied to a wind turbine blade. Using luminescent mini-
tufts, Chen et al. conduct a quantitativ e analy sis of the tuft
inclination angle on a flat plate (Chen et al. 2019 ) and a
bac kw ard-f acing step (Chen et al. 2020 ).
While all af orementioned studies aimed at e xtending t he
classical tuft visualization techniq ue to extr act quantitativ e
flo w field inf or mation, a method that can be easily adapted
b y other researc hers has not been presented to the best of our
kno w ledg e. Fur t her more, there appear to be no attempts to
relate the tuft deflection to t he momentum of the flow and
thus allow f or the measurement of the flow v elocity .
The objectiv e of this paper is t heref ore to introduce a
method that is easily adaptable b y other researc h g roups and
allo w s to e xtract quantitativ e v elocity data from captured
tuft images without the need f or commercial software. The
basic pr inciple is demonstrated b y means of tw o e xamples,
representing surface and off-surface applications. F irst,
unsteady near -w all quantities are obtained in a turbulent
separation bubble (TSB) b y affixing tuf ts to the wall in a
one-sided diffuser . Then, the turbulent w ake of an Ahmed
body is in ves tigated b y means of a tra v ersable probe with a
larg e number of tuf ts.
2 Ev aluation routine
The basic e valuation r outine f or tuft deflection velocimetry
(TD V) is ex emplar ily displa y ed in Fig. 1 . Note that a mini-
mum w orking e xample of the algorit hm is also pro vided with
the supplement ar y mater ial. Follo wing the application of tuf ts
inside a giv en flo w field, the first step in obtaining quantitativ e
inf or mation consists in the recording of images. A prior i, the
method is not limited to coherent snapsho ts but t he acquisition
rate of the camera must be adjusted to the time scales associ -
ated with relev ant unsteady flo w f eatures in order to study the
dynamic flo w beha vior . Sufficient lighting is requir ed so t hat
tufts are captured in their entirety . This can be par ticularl y
challenging in the case of high acq uisition rates and lo w expo -
sure times. In practice, tufts of UV activ e mater ial illuminated
with appropr iate LED ar ra ys are successfull y emplo yed in this
scenar io. Based on recorded images, the g eometries of indi -
vidual tufts can be extracted. Since the y are typicall y v er y thin
compared to their length, the tuf t edges can be considered a
satisfying representation of the tuf t deflection. T o e xtract these
edges, the intensity gradient field is ev aluated. While t here

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are se v eral different approaches, w e f ound t he Pr e witt method
( 1970 ) to be the most accurate and cos t-efficient f or the dem -
onstration tes t cases addressed in the f ollowing.
The Pr ewitt operator employ s tw o
3 × 3

kernels that are
con vol ved with an imag e to appro ximate the intensity der iva -
tiv es in hor izontal and vertical direction, respectivel y . This
separable approac h makes it efficient but ma y also cause inac -
curacies when dealing with high-frequency v ar iations in the
intensity function. Theref ore, a sufficient contrast needs to be
ensured betw een tuf ts and back ground. In experiments, this
is typicall y achie v ed b y applying a blac k f oil or coating to the
bac kground if required. The Pr ewitt filter then retur ns a zero-
gradient f or such a bac kground whereas the inter face be tween
tuft and back ground is detected as an edge and will be re tur ned
in a binar y image (s tep 2 in Fig. 1 ). This binary image then
undergoes a Hough tr ansf or mation (step 3), a robust s tandard
procedure to e xtract parametr izable geometries (Duda and
Har t 1972 ). In t he case of line extr action required f or TD V ,
the Hough space is spanned by the Euclidean distance of the
line
𝜚

and the angle betw een the per pendicular of the line and
the abscissa
𝜗

. Thus, the line can be represented by its Hesse
nor mal f or m
(1)
𝜚 = x cos 𝜗 + y sin 𝜗 .

It is w or th noting that t he angle giv en in the Hesse nor -
mal f or m already is an indicator f or the tuf t or ient ation.
Ho we ver ,
𝜗

depends on the dimensions of ra w images
since the location of the abscissa wit h respect to the tuf t/
e xtracted line ma y be varied. Theref ore, we emplo yed
a trac king method to detect the end points of the para -
metrized lines (step 4) and computed the tuf t deflection
angle based on their locations. For cer tain applications
such as the second demonstr ation ex ample in this ar ticle,
it is also necessar y to compute the length of t he detected
lines which inher ently req uires kno w ledge regar ding t heir
end points as w ell.
Repeating this procedure f or multiple successiv e
images, t he time-dependent deflection angle of tufts can be
der iv ed f or fur ther st atistical anal ysis of a giv en flow field.
3 Choosing tuf ts withappropria te
proper ties
The accuracy of TD V is directly dependent on the c har -
acter istics of the emplo y ed tuf ts. A br ief summar y of the
main parameters that need to be considered f or tuf t selec -
tion is giv en in this section.
Fig . 1 Flo w diag ram visualizing the ev aluation of the deflection angle of one tuf t

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3.1 T uft visibility
Being an optical measurement tec hnique, good visibility
of the tuf ts is requir ed, ensur ing t hat the tuf t geome tr y is
adequatel y represented in pixel space. F or a giv en lighting
setup, tw o parameters ma jorl y affect the visibility: (a) the
tuft t hic kness and (b) its color/reflectivity .
T o reduce t he influence on the flow field, tufts of mini -
mum dimensions are pref er red. This minimum extent
strongl y depends on t he optical resolution of the measure -
ment setup, i.e., the size of the measurement domain and
the camera chip. A lo w resolution can be compensated by
a br ight tuft color which is e x emplar ily demons trated in
Fig. 2 where tufts of different mater ials but similar diam -
eters are sho wn. Whereas t he images of transpar ent tuf ts of
pol yamid (P A) monofilament and n ylon are associated with
lo w contrast, the other tufts clearly r eflect a g reater amount
of light and are theref ore better suited f or the measurement
techniq ue.
3.2 Static beha vior oftufts
For a specific flo w momentum, the deflection angle of a tuft
is determined by its length and stiffness. A gain, long er tufts
are not desired due to t he greater influence on the flow field
and because the velocity inf or mation is integrated across
greater spatial scales. On the other hand, shor t tufts are typi -
call y not suited f or low -speed measurements as t he deflec -
tion angle is small compared to the measurement accuracy
in this case.
The char acter istic deflection cur v es f or tufts of lengt h
l = 10 mm

are sho wn in Fig. 3 . T o compile t hese cur v es,
a nozzle w as supplied with a constant mass flow rate,
resulting in a steady flo w approaching the tufts. The noz -
zle diameter w as larg er than t he tuft lengt h, and it w as
ensured that the entire tuf t w as located inside the poten -
tial core of the steady jet. Se veral tufts w ere tested f or
each material, which enabled calculating bo th t he mean
deflection angle and the relative scatter f or each tuft, indi -
cated as er ror bars. Ev en though tuf ts were nominall y
or iented per pendicular to the nozzle axis in t he absence
of the jet (
U ∞ = 0 m/s

), small offse t angles occur red
occasionall y . These were de ter mined wit h the introduced
method and subtracted from the deflection angles meas -
ured subsequentl y .
Due to their g reater stiffness, the smallest deflection
angles are f ound f or poly amide (P A) and ny lon. How ev er,
the range of deflection angles is muc h greater f or n ylon
where the variance at
U ∞ = 20 m/s

is 98% of the mean
v alue
𝜑 ≈ 17.1 ◦

. The relativ e scatter f or P A is 32% at the
same inflo w v elocity . The poly ester (PES) tufts exhibit a
similar total v ar iance of up to
Δ 𝜑 = 10 ◦

but the relativ e
v ar iation is smaller due to greater ov erall deflection angles
(24% at
U ∞ = 20 m/s

). The same is true f or t he cotton
tufts t hat are associated with the larg est deflection angles,
yielding a relativ e de viation of 12% at
U ∞ = 20 m/s

. Ev en
though t his resembles the best reproducibility of tuft mate -
r ials assessed in this study , the v alue is still inf er ior com -
pared to other quantitativ e measurement techniques. The
relativ el y low degree of reproducibility can be attributed
to a number of causes whic h must be addressed in more
detail in future studies. Firs t, the tuf ts used in t his study
are not g eometrically identical, mainl y due to slight pre-
def or mations induced when handling and cutting them.
Fur ther more, manufacturing imper f ections affect t he tuft
proper ties in the case of braided tufts. In addition to t hat,
they w ere affixed with adhesiv e tape and t he identical
or ientation cannot be ensured in the process. Ho we v er ,
v ar ying tuf t characteristics can be compensated b y estab -
lishing different calibration la ws f or individual tufts. This
w as done f or t he second demonstration case presented in
Sect. 4 .
Among the assessed mater ials, cotton tufts e xhibit t he
most f a v ourable characteristics and will be emplo y ed in the
f ollowing.
PA

(white)
PA

(monofil.) Nylon
PES

(neon, white, UV active) Cotton
Fig . 2 V isibility of different tuft mater ials of similar diameter f or
equal lighting conditions
0
10
20
30
40
PA (white)
Nylon
PES (UV active)
Cotton
ϕ
(°)
0 5 10 15 20 25
U
∞

(m/s)
Fig . 3 T uft deflection angle as a function of velocity f or different tuft
materials

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3.3 Dynamic behavior oftufts
Since a steady approac h flo w only reflects the conditions
of a limited number of flo w configurations, fur ther gener ic
tests w ere conducted to address the dynamic beha vior of
tufts exposed to uns teady flo w . F or t his pur pose, a pulsed
jet actuator consis ting of a solenoid val ve and a nozzle w as
emplo y ed and star ting jets w ere emitted at constant freq uen -
cies. Figure 4 sho ws the time signal of the deflection angle
of a cotton tuft of
l = 5 mm

(open circles) f or a frequency of
f = 50 Hz

and the velocity signal measur ed wit h a hot wire
sensor as a ref erence method. The tuf t is clearl y capable
of f ollowing the dominant frequency . This w as obser ved to
be the case f or frequencies up t o
f = 80 Hz

. Theref ore, a
dynamic response req uired f or man y lo w -speed applications
can be attested. Ho we ver , it is w or t h pointing out that t his
generic test configuration does not reflect highl y turbulent
flo w s wit h flo w f eatures cor responding to larg e frequency
bands. The suitability f or these cases may be addressed in
future applications.
4 Demonstra tion ofapplicabilit y
T w o test cases wer e in v estigated with the proposed measure -
ment techniq ue to demonstrate its capabilities: (1) the near -
w all flo w along a turbulent separation bubble (TSB) and (2)
the w ake of a g ener ic car model.
4.1 T est c ase 1: turbulent separa tion bubble
TSBs are g enerated when a turbulent boundar y la y er sepa -
rates from the w all and reattaches furt her do wnstream,
enclosing the separation zone. The f lo w separation can
either be induced by a g eometric singular ity , such as a bac k -
w ard f acing step (e.g., Driver e tal. 1987 ; Ma and Schr öder
2017 ) or f ence (e.g., Ruder ich and F er nholz 1986 ; Hudy and
N aguib 2003 ) or b y an adverse pr essure g radient (APG).
In this test case, a pressure-induced TSB w as in v estigated
where the APG w as introduced b y the widening of t he test
section cross area. A similar flo w configuration w as in ves -
tigated in W eiss et al. ( 2015 ) and Mohammed- T aif our and
W eiss ( 2016 ) on t he basis of unsteady pressure, HW A and
PIV measurements.
In the cur rent study , the free stream v elocity was
U ∞ = 20 m/s

. The mean flo w field of the TSB addressed in
this study is sho wn in Fig. 5 . The time-a verag ed recircula -
tion zone associated with the TSB is enclosed by the sepa -
rating streamline
 u = 0 m/s

, spanning a region of roughl y
x ≈ 0.1 … 0.45 m

.
Cotton tufts (
l = 15 mm

) w ere attached to the test sec -
tion surface inside the symme tr y plane with a spacing of
Δ s = 25 mm

as indicated in the sample photograph y shown
in Fig. 5 . A second line of tufts with free ends pointing in t he
other direction w as used f or ref erence. While they sho wed
good agreement with tuf ts placed on the symmetr y plane,
w e will not address them in much detail here. The main
0
10
20
30
40
t (s)
U

∞
(m/s)

0.02 0.04 0.06 0.08
100

75
50
25
0
ϕ
(°)
Fig . 4 Dynamic beha vior of tuft subjected to
f

=
50 Hz

pulsed jet,
hot wire signal sho wn in gray color f or ref erence
0
1
Side view
u = 0 m/s
0
-0.1
0.1
y (m)

0.5
u U / (-)

∞
U ∞
α = 21°
x (m)
Diffuser ramp Surface tuft array
00 .1 0. 20 .3 0. 40 .5 0.6 -0.1 0.7 0.8
0
z (m)
T op view
U ∞
U ∞
Diffuser ramp
Fig . 5 T SB studied by means of TD V ; time-a v eraged stream wise
v elocity field measured with PIV (top), application of sur face tufts in
symmetry plane (bottom)

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objectiv e in this scenar io was t o identify t he instantaneous
flo w direction and detect unsteady regions of re verse flo w in
par ticular . Theref ore, t he tufts were attached perpendicular
to the main flow dir ection. Images of the tufts were taken
at an acquisition rate of
f = 200 Hz

o v er a time duration of
Δ t = 10 s

. Due to the size of the relev ant flo w region, the
tuft ar ra y w as divided into f our segments of similar lengt h
of which imag es were taken subseq uently . T o compensate
the tilted diffuser ramp sur f ace, the camera was adjus ted so
that t he optical axis w as parallel to the w all nor mal f or all
segments.
With initial tuft angles being transv erse to the free stream
direction, def lection angles of
𝜑> 0 ◦

are e xpected f or
regions of f or ward flo w , whereas flo w recirculation yields
angles of
𝜑< 0 ◦

. It is w or t h mentioning that the locations
of separation and reattachment are no t constant but fluctuate
significantl y . This is explained b y t he finding that TSBs are
char acter ized by a lo w-freq uency contraction and e xpansion
in addition to medium-freq uency oscillations associated wit h
v or tex s tr uctures inside the separated shear lay er and high-
frequency fluctuations caused b y t he turbulent nature of the
flo w (Mohammed- T aif our and W eiss 2016 ). Theref ore, the
test case is suited to assess the capability of the TD V method
to measure unsteady flo w conditions in close w all pro ximity .
Figure 6 sho ws the time-a v eraged deflection angles o f
tufts along t he diffuser axis that are based on the time sig -
nals of tuft deflection angles obtained wit h the procedure
introduced in Sect. 2 .
As e xpected, the region upstream of the diffuser ramp
(
x < 0m

) is characterized by positiv e deflection angles of
𝜑> 15 ◦

cor responding to the f or w ard-flow boundar y lay er .
Fur ther downs tream, the flow decelerates and the tuft deflec -
tion angles decrease accordingl y . A mean v alue of
𝜑 ≈ 0 ◦

,
i.e., an a verag e tuft or ient ation per pendicular to the diffuser
axis, is f ound at
x ≈ 0.15 m

while negativ e deflection angles
are obser v ed in the range of
x = 0.15 … 0.45 m

due to flo w
recirculation in this region. This cor responds reasonabl y
w ell wit h the mean separation line, extracted fr om PIV
measurements, that is sho wn in Fig. 5 . Downs tream of the
TSB, v or tex structures are shed onto the w all and positiv e
deflection angles are observed.
Being a c haracter istic quantity f or the dimensions of
TSBs, the f or ward flo w coefficient
𝛾 ( x )

w as deduced. This
quantity repr esents t he time per iod dur ing which the flo w is
or iented in stream wise direction (
u > 0 m/s

) relative t o th e
total obser v ation time (Simpson 1996 ). Here, it w as appro xi -
mated b y the number of samples where
𝜑> 0 ◦

relativ e to the
total number of samples (Fig. 7 ).
The e valuation of tuft angles yields tw o regions of
𝛾> 99 %

, being
x ≤ 0m

and
x ≥ 0.5 m

. The respectiv e
boundar ies mark the positions of incipient detachment and
complete r eatt achme nt as defined by Sim pson ( 1996 ). The
cor responding length of t he enclosed TSB is
L 99 ≈ 0.5 m

which is about 20% smaller than the v alue measured with
PIV where the complete reattachment point w as not inside
the measurement domain but a location of
x ≈ 0.6 m

can be
assumed. The main reason f or t his de viation is t he difference
in f or ward flo w coefficients at t he do wnstream end of the
TSB. Whereas PIV measurements re veal a number of ins tan -
taneous snapshots where recirculation occurs, this inf or ma -
tion is not cap tured by T D V . The negativ e stream wise v eloc -
ity component is induced b y v or tex s tr uctures or iginating
from the separated shear la y er and the time duration may
be too shor t to cause negativ e deflection angles. How e ver ,
smaller tuft dimensions may be able t o render this process
more accuratel y . The same effect is present inside the TSB
30
20
10
0
-10
0 0.2 0.4 0.6 0.8
x (m)

φ (°)
U ∞
φ
Fig . 6 Mean tuft deflection angles along diffuser axis
0
20
40
60
80
100
0 0.2 0. 40 .6 0.8
x (m)

γ( %)
TDV PIV
Fig . 7 Forw ard flow r atio along diffuser axis deter mined by means of
TD V and PIV , respectiv ely

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where PIV measurements sugg est f or ward flo w coefficients
of
𝛾 PIV ≈

15
%

whereas tuft deflection angles are negativ e at
almost all times, hence
𝛾 T DV ≈ 0 %

. Ho we ver , the locations of
transitor y detachment and r eatt achment mar ked b y
𝛾 =

50
%

are w ell captured by the tec hnique introduced in this ar ti -
cle, and a TSB length of
L 50 ≈ 0.38 m

is der iv ed both from
PIV and TD V measurements. It should be noted, ho we ver ,
that the location of transitor y detachment as derived from
the f or w ard flo w ratio is slightly ups tream of the location
where
𝜑 = 0 ◦

. This can be explained b y t he f act that close
to the location of transitor y detachment, the magnitude of
deflection angles is lar ger in the case of f or war d-flow e ven
though the respective time duration is eq ual to that of rev erse
flo w . Since t his w as not observed in PIV measurements, w e
attr ibute this finding to individual tufts having a pr ef erential
bending direction.
Finall y , the fluctuation le vel of tuft deflection angles is
e valuated along the TSB. As a ref erence, unsteady pressur e
measurements are conducted with piezo-resistiv e pressure
transducers. Both distributions are sho wn in Fig. 8 . In good
agreement with results in t he literature (Mohammed- T aif our
and W eiss 2016 ), two local peaks are f ound close to the
mean locations of separation and reattachment. This is also
reflected b y the TD V anal ysis where maxima of the order
of
r ms ( 𝜑 � )≈ 6 ◦

and
r ms ( 𝜑 � )≈ 13 ◦

are f ound, respectivel y .
Generall y , the first test case sho ws that the method is w ell
suited to adequatel y detect the instant aneous flo w direction
when applied in the near -w all region. Fur t her more, an anal y -
sis of unsteady flo w was successfull y conducted to deter -
mine regions of maximum fluctuation le vel inside a flo w
configuration. The freq uency peak associated wit h these
fluctuations w as in the region of
f ≈ 60 … 80 Hz

. Ho we ver ,
er rors occur when the flo w is dominated by h igher -frequency
flo w rev ersals.
4.2 T est c ase 2: wak e ofgeneric car model
A second test configuration w as chosen to assess the perf or -
mance of the TD V method when a free velocity field is ana -
l yzed, i.e., when the tuf ts are not attached to a solid surf ace.
For this pur pose, an Ahmed body—a generic car geometry
introduced in Ahmed etal. ( 1984 )—w as studied inside the
same lo w -speed wind tunnel as the TSB (test case 1) at a
free stream v elocity of
U ∞ = 20 m/s

. Based on the height
of the
50 %

scale model
H ≈ 0.14 m

, t he Re ynolds number
w as
Re H ≈

1.9 ⋅ 10
5

. The w ake topology subject to a v ar ied
slant inclination angle
𝛽

is w ell known fr om previous s tud -
ies (Ahmed et al. 1984 ). The smallest drag coefficient is
f ound at
𝛽 ≈ 10 ◦

where the flow is attac hed on the slant sur -
f ace. The drag then increases f or greater inclination angles
due to the enhancement of stream wise v or tices or iginating
at the c-pillars. At a slant angle of
𝛽 ≈ 30 ◦

, t hese v or tices
break do wn and a discontinuous drop in drag occurs. While
the larg e-scale stream wise v or tices will not be addressed in
this study , w e emplo y ed TD V to in ves tigate the influence
of the slant inclination on the dimensions of t he recircula -
tion zone inside the symmetr y plane. The setup f or this test
case is schematicall y depicted in Fig. 9 . T w o slant angles,
𝛽 = 15 ◦

and
𝛽 = 35 ◦

, were in v estigated and a probe with
50 cotton tufts of
l = 5 mm

length w as tra v ersed in the
symmetry plane in
Δ x = 4 mm

steps along the x direction
betw een
x =− 100 … 200 mm

where
x = 0 mm

marks the
base of the Ahmed body . The probe consisted of a solid
beam with dr illed holes t hrough whic h the tuf ts were s tic ked
and glued on the back side of the probe. The v er tical spacing
betw een neighbor ing tufts was
Δ y = 4 mm

. The optical axis
of the camera w as nor mal on the symmetr y plane (Fig. 9 ) ,
and images w ere t aken o v er a duration of
Δ t = 3s

with an
0
3
6
9
12
15
0 0.2 0.4 0.6 0.8
x (m)

rms( ‘) (°) φ
0
0.04
0.08
0.02
0.06
0.1
rms( ) (-) c‘
p
TDV
Pressure transducer
Fig . 8 Fluctuation le v el along diffuser axis determined by means of
TD V and piezo-resistive pr essure transducer, r espectivel y
Ahmed body
T raversable TDV probe

with 50 tufts
U ∞
Splitter plate

Camera
x
y
Fig . 9 Se tup f or flow field measurement of Ahmed body w ake b y
means of TD V

Experiments in Fluids (2020) 61:146
1 3
146 Page 8 of 11
acquisition rate of
f = 400 Hz

. This w as sufficient to resol v e
rele vant shedding modes that are associated with a Str ouhal
number of
St ≈ 0.22

at
𝛽 = 35 ◦

according to T una y et al.
( 2014 ), cor responding to a frequency of
f ≈ 30 Hz

.
Measurements w ere conducted inside the symmetr y plane
where the out-of-plane component is assumedl y negligible.
The initial tuft or ient ation w as parallel to the z axis, and the
tufts were free to mo ve in tw o directions, namely x and y
in this application scenar io. The ev aluation algor ithm w as
theref ore e xtended to compute tw o separate deflection angles
cor responding to both in-plane v elocity components in the
symmetry plane. As indicated abov e, t he initial or ientation
of the tuf ts w as almost parallel with reg ard to the optical
axis, resulting in almost zer o lengt h when imaged b y t he
camera. The projected length of the tufts w as used to obtain
deflection angles. Ag ain, 2D2C PIV measurements wer e
emplo y ed as a ref erence measurement techniq ue. Here, mean
v alues of the two v elocity components wer e obt ained based
on 500 incoherent snapshots. The dis t ance betw een v ectors
measured with PIV w as
Δ x =Δ y ≈ 1 mm

, yielding a f our
times finer resolution than f or TD V measurements.
Since the preliminar y analy sis sho wed that the charac -
ter istic tuft deflection cur v e is not identical f or different
tufts, an initial calibration w as per f or med by appl ying dif -
f erent flow v elocities rele vant to this tes t case and measur -
ing the individual deflection angles in the absence of t he
Ahmed body . The characteristics of individual tufts were
then mapped with second-order polynomials sho wn in
Fig. 10 . Since the cotton tufts used f or this test case were
shor ter than t hose addressed in Fig. 3 , the deflection angles
are smaller at eq ual veloc ities. The tw o in-plane v elocity
components u and v were computed based on the individual
calibrations where the free stream v elocity was v ar ied in
the range
u = 0 … 25 m/s

(Fig. 10 ). Identical characteristics
w ere assumed f or negativ e velocities in main s tream direc -
tion and f or t he v er tical v elocity component. In hindsight,
this assumption is probabl y not justified as a pref erential
direction of the tuf ts w as indicated b y results of the previ -
ous test case where different deflection angles occur f or the
same f orcing.
Generall y , the additional effor t required f or this calibra -
tion w as minimal since no modification to the experimental
setup w as needed in ter ms of the optical ar rang ement.
The main results of this experiment are sho wn in Fig. 11
where the contour field of the nor malized stream wise veloc-
ity component is o v erla y ed with t he time-a verag ed stream -
line patter n that is based on the measured vector fields.
The longitudinal e xtent of the detected recirculation
zones measured with TD V ag rees well with the length
obtained wit h PIV measurements. The stagnation point is
located at
x ≈ 150 mm

f or t he
𝛽 = 15 ◦

slant angle whereas
a longer r ecirculation zone is f ound f or
𝛽 = 35 ◦

where the
stagnation point is at
x ≈ 180 mm

. Fur t her more, the upper
par t of the vortex ring rooted at the base is captured b y the
method. Ho we ver , t here is a lar ge difference in the v elocity
magnitude inside the recirculation zone determined by both
methods. The approac h introduced in this ar ticle suggests a
minimum longitudinal v elocity of
u ≈− 0.6 U ∞

compared to
u ≈− 0.4 U ∞

obtained from PIV measurements. In general,
there is a systematic difference be tween bo th measurements
of the order of
Δ u =( u PIV − u T DV )∕ U ∞ > 0.1

inside the
recirculation zone. A significant de viation of opposite sign
in ter ms of the stream wise v elocity inside t he shear la y ers
bounding the recirculation zone is also obser v ed. This ma y
be attr ibuted to the small v elocity magnitude
| u |

→
0 m/s

present in these regions. As a result of this inaccuracy , the
recirculation zone measured with TD V is systematicall y
smaller in v er tical direction.
None theless, t he second test case demonstrates that the
TD V techniq ue can be emplo yed t o gain a quantitativ e
impression of a 2D2C flo w field with a measurement setup
that is much easier , cheaper and simpler to establish com -
pared to PIV measurements. The measurement accuracy
ma y be adequate f or a preliminar y assessment of comple x
flo w s, t hough it is probabl y inacceptable f or detailed analy -
ses. This insufficiency is mainl y linked with the mater ial
proper ties of the cotton tufts used in this study .
5 C onclusions
The main objectiv e of this ar ticle w as to introduce a no v el
measurement method that allo ws f or a quic k and simple
quantitativ e anal ysis of flo w fields. T w o test configura -
tions ha ve demons trated the potential of t his approac h.
Ho we ver , t he cur rent limit ations preclude a replacement of
0
10
20
30
40
φ (°)
05 10 15 20
U
∞

(m/s)
Fig . 10 Second-order pol ynomials for v elocity calibration of individ-
ual tufts, mean value printed bold

Experiments in Fluids (2020) 61:146
1 3
P age 9 of 11 146
con ventional measurement tec hniques. W e theref ore hope
that the approach is adapted and modified b y other researc h -
ers, gradually optimizing the method as has been done with
other measurement tec hniques in the past.
5.1 Adv antages anddisadv antages
The main adv ant age of TD V lies in its q uick and sim ple
implementation. No elaborate measurement eq uipment
is requir ed and the dat a processing is f ast compared t o
other techniq ues f or flow field measurements. A camera
is on hand in practicall y all research f acilities, and the
data analy sis can be per f or med on a standard w ork station.
In addition to that, the method can be e xecuted b y new
users after a very shor t initial training phase due to the
intuitiv e function pr inciple. At the same time, the r isk of
committing f atal er rors with conseq uences f or the healt h
of the user or damages of eq uipment dur ing that training
phase is v er y low . As another main adv antage, inf or mation
regarding lar ge flo w fields can be obtained in a relativel y
shor t amount of time compared to pointwise measurement
techniq ues and also PIV where the measurement domain is
-0.5
0
0.5
1
x (mm)

50
100
150
y (mm)
50
100
150
y (mm)
0 5 -0 100 50 150
TDV
PIV
/ (-)

∞
x (mm)

0 5 -0 100 50 150
β = 15°
β = 15°
β = 35°
β = 35°
Deviation
β = 35°
β = 15°
50
100
150
y (mm)
-0.5
0
0.5
(- ) / (-) uu U
PI VT DV ∞
Fig . 11 V elocity field in the wak e of an Ahmed body; measured with TD V (top row) and PIV (center r ow) and de viation between v elocity fields
obtained with both methods (bottom ro w); stagnation point marked with red cross

Experiments in Fluids (2020) 61:146
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146 Page 10 of 11
typicall y smaller due to a limited region of sufficient laser
light energy and a s trong er reliance on optical resolution
to render seeding par ticles.
These potential benefits are currently offse t by an insuf -
ficient measurement accuracy that is mainl y due to a v er y
limited reproducibility of the tuft characteristics. While
not directl y addressed in t his ar ticle, TD V is an intr usiv e
method and the user must be a w are that required instru -
mentation, e.g., probes and tufts, may ha v e a significant
influence on the flow field. Fur t her more, tufts of one spe -
cific geome tr y are onl y suit able to a cer tain range of flo w
v elocities so that an appropr iate tuft mater ial and length
must be c hosen according to the relev ant velocity r ange.
The results of this study ha ve also sho wn t hat the tech -
nique ma y not be suited f or flow s dominated by f eatures
at time scales associated with frequencies of
f > 100 Hz

.
As with ev er y other experiment al techniq ue, an inte -
gration along a specific spatial domain is per f or med. For
the TD V method, t his domain is equal to the tuft which
will usuall y ha v e greater dimensions t han the integ ration
regions f or other methods. It is t heref ore an inherent chal -
lenge of the TD V techniq ue to assign measured v elocity
v ectors to defined locations in the flow field. This difficulty
is amplified when tufts are strongl y bent or ev en twisted.
As a gener al r ule, ev er y attempt should be made to a v oid
such def or mations, f or inst ance b y using tuf ts that are as
shor t as possible and by appl ying t hem with an adequate
or ientation.
5.2 P otential fields ofapplication
As mentioned in the previous section, the method proposed
in this ar ticle is cur rentl y not able to substitute a classical
measurement tec hnique. W e t heref ore advocate an em ploy -
ment in a supplemental manner , e.g., f or preliminar y anal -
yses to narrow do wn the parameter space f or subsequent
measurements.
Being a method capable of deli vering inf or mation regard -
ing larg e flow fields in relativ ely short amounts of time, TD V
ma y nonetheless be readil y utilized where PIV measure -
ments are precluded. This ma y be t he case when no PIV
sys tem is on hand in the first place or when PIV cannot be
emplo y ed f or saf ety reasons, e.g., outdoors or when contami -
nation with seeding par ticles is not desired. Fur ther more,
TD V is conceptually no t restricted to two-dimensional meas -
urement domains as tufts ma y be att ached t o cur ved surf aces
with images readil y dew ar ped if req uired.
Generall y , there is a v er y larg e number of potential appli -
cation scenar ios, including near -w all measurements but also
an emplo yment inside w all-distant flo ws, and we hope that
this will be reflected in future studies b y other research
groups.
5.3 Outlook
Future effor ts must be primar ily aimed at impro ving t he
measurement accuracy of the method proposed here. From
our point of vie w , this can be achie v ed by identifying a tuft
mater ial with more reproducible properties. In t he cur -
rent study , cotton tufts were utilized, e xhibiting drasticall y
v ar ying mechanical properties despite t heir geome tr ic sim -
ilar ity . W e also observed that occasionall y , the character -
istic deflection beha vior chang ed o ver time as irrev ersible
def or mation of t he tuf ts occur red after being exposed to
the flow im pulse. W e theref ore fir mly belie v e that signifi -
cant impro vement can be br ought about b y identifying a
more appropriate tuf t mater ial.
Acknowledgements Open Access funding pro vided by Pr ojekt DEAL.
The authors gratefully ac know ledge the assistance from Steffen F eld -
hus and Y annick Kather with wind tunnel measurements f or the first
demonstration case.
Code a vailability A minimum w orking e xample of the algorithm intro -
duced in this ar ticle is pro vided with t he supplementar y mater ial.
C ompliance with ethical standards
Conflict of interest The authors declare that t he y ha ve no conflict of
interest.
Open Acc ess This ar ticle is licensed under a Creative Commons A ttri -
bution 4.0 Inter national License, which permits use, shar ing, adapta -
tion, distribution and reproduction in an y medium or f or mat, as long
as you giv e appropr iate credit to the or iginal author(s) and t he source,
pro vide a link to the Creative Commons licence, and indicate if c hanges
wer e made. The images or other third par ty mater ial in this ar ticle are
included in the ar ticle’ s Creativ e Commons licence, unless indicated
otherwise in a credit line to t he mater ial. If material is not included in
the ar ticle’ s Creativ e Commons licence and your intended use is no t
per mitted b y statutor y regulation or ex ceeds t he per mitted use, you will
need to obtain per mission directly fr om the copyr ight holder . To vie w a
copy of this licence, visit http://creat iv eco mmons .org/licen ses/b y/4.0/ .
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