-
mAccepted 20 May 2008
Keywords:Dual triangulate bluff bodyVortex shedderStrouhal
number
size for a range of separations between 35 and 65 mm. The
Reynolds number varies in the range of6.621031.99105. The vortex
shedding frequencywas obtained on the basis ofmeasured
fluctuatingpressure on the lateral side of the vortex shedder by a
piezoelectric press sensor. Those results led to thefollowing
conclusions: (1) the linearity of Strouhal numbers of dual
triangulate bluff body combinationsvaries with the opening length
of two bluff bodies and diameters of the bluff bodies. The best
linearityis the same as that of a single bluff body. (2) The best
size of a dual triangulate bluff body was found as:If the pipe
diameter is D, the diameters of the first and second bluff body are
0.26D and the height ofthe bluff bodies is 0.34D. (3) For a dual
triangulate bluff body, the optimal opening length is equal to
thedistance between consecutive vortices of flow over single bluff
body. Our results will be valuable in theflow measurement and
instrument design of vortex flowmeters in industries.
2008 Elsevier Ltd. All rights reserved.
1. Introduction and background
The phenomenon of vortex shedding frombluff bodies has
beenstudied since the pioneering work of Strouhal (1878) and
VonKarman (1912). When a bluff body is placed in a flow
stream,vortices shed alternately from each of the side surfaces of
the body.The non-dimensional shedding frequency, the Strouhal
number, isdefined as:
S = fdUm
(1)
where f is the vortex shedding frequency, d is the bluff body
diam-eter, and Um is themean free-stream velocity. Over a wide
range ofReynolds numbers, the Strouhal number is a constant
[1,2].Shaw [3,4] found that the vortex shedding frequency is
about
3a/2pid, where a is the speed of sound and d is the diameterof
the body. The shedding vortex oscillating at this frequencysends
back pulses of the attached layer. Due to Dopplers ef-fect, the
frequency is then reduced by a ratio of 1 (u us)/a, where us is the
velocity of vortices relative to streamvelocity, and u is the
velocity of vortices. An interaction
Corresponding author. Tel.: +86 13408604905.E-mail addresses:
[email protected], [email protected] (J. Peng).
takes place between the acoustic vibration of the attached
flowwith the original frequency and the sending vortex,
whichproduces strong pulses with a beat frequency of 3a2pid (
uusa ).
Those strong pulses cause the shedding of a vortex. The
shed-ding frequency of the vortex pair is then ( 12 )(
32pid )(u us),
and the Strouhal number will be:
S = 34pi
(1 us
u
). (2)
From experiments, the distance between consecutive vortices, l,
is4pid/3 [5].Roshko [6] first proposed the idea of building a
flowmeter based
on the assumption of a constant Strouhal number [6]. He
studiedvortex shedding from a circular cylinder in a Reynolds
numberrange of 40104. For Re > 300 (the irregular range), the
Strouhalnumber remains at an almost constant value of 0.2,
independentof the Reynolds number. Roshko (1961) also showed that
as Reincreases beyond a critical value of 2 105 for a circular
cylinder,the Strouhal number increases rapidly. Gerrard [7]
explained thatthe constant Strouhal number results from a balance
betweentwo length scales in the near-wake; shear layer the
thickness(diffusion length) and vortex formation length, i.e. the
distancebehind the bluff body at which entrained fluid first
crosses thewake centerline. Bearman [8] suggested that the lateral
distancebetween vortex rows is an appropriate characteristic length
scale.Flow Measurement and Instru
Contents lists availa
Flow Measurement a
journal homepage: www.else
Experimental investigations of Strouhal nbluff bodiesJiegang
Peng a,, Xin Fu b, Ying Chen ba School of Automation, University of
Electronic Science and Technology of China, Chengdub The State Key
Laboratory of Fluid Power Transmission and Control, Zhejiang
University, H
a r t i c l e i n f o
Article history:Received 28 March 2007Received in revised form8
May 2008
a b s t r a c t
Experimental studies were cin a circular pipe 50 mm inthe
Strouhal number of nine0955-5986/$ see front matter 2008 Elsevier
Ltd. All rights
reserved.doi:10.1016/j.flowmeasinst.2008.05.002entation 19 (2008)
350357
ble at ScienceDirect
nd Instrumentation
vier.com/locate/flowmeasinst
umber for flows past dual triangulate
, Sichuan 610054, PR Chinaangzhou, Zhejiang 310058, PR China
arried out on the Strouhal number for flow past dual triangulate
bluff bodiesdiameter. Results are presented of an experience
instrument evaluation ofdual combinations based on triangulate
bluff body geometries of different
-
J. Peng et al. / Flow Measurement and
Nomenclature
S Strouhal number (dimensionless number)f the vortex shedding
frequency (Hz)d the bluff body diameter (mm)b body height (mm)Um
the mean free-stream velocity (m/s)a the speed of sound (m/s)d body
diameter (mm)us velocity of the vortices relative to stream
velocity
(m/s)u velocity of the vortices (m/s)l1 First Bluff body height
(mm)l2 Second Bluff body height (mm)D inner diameter of circular
pipe D = 50mm (mm)L0 5 m, length of circular pipe (m)Sc blockage
ratio (dimensionless number)Q the volume flow rate (m3/h)Re
Reynolds number (dimensionless number) kinematic fluid viscosity
(m2 s1)where = 1.51
105(m2 s1) (air, t = 20 , Standard AtmosphericPressure)
d1 First Bluff body diameter (wide) (mm)d2 Second Bluff body
diameter (wide) (mm) the error of the Strouhal number (%)N the
number of test UmS the Strouhal number mean value
(dimensionless
number)Si the Strouhal number of No.i UmL opening length of two
bluff bodies (mm)l the distance between consecutive vortices (mm)K
L/l, the relationship between l and L
The vortex flowmeter based on vortex shedding emerged in
theearly 1970s. Since there is nomoving part in this flowmeter,
little isconcerned for the wear or physical damage by foreign
matter. Thelow-pressure drop across themeter also results in low
energy cost.[9]. In addition, it has a number of attractive
advantages like highreliability, low maintenance, and insensitivity
to fluid propertiesand temperature. A Karman vortex flowmeter is
widely used in themeasurement of flow rate in a pipe flow. In this
method, the flowrate is measured by the vortex shedding frequencies
from a two-dimensional cylinder.However, the vortex flowmeter has
its own defect like poor
noise immunity and low-flowrate sensitivity. Thinh et al.
[10]proved that the ambient noise as well as the inherent
pressurefluctuation from the measured system could considerably
reducethe measurement accuracy through experiments. On the
otherhand, the sufficiently high signal-to-noise ratio (SNR) cannot
beachieved by a piezoelectric press sensor in lower Reynolds
number,which results in a limited measuring range for the vortex
flowrate.In order to improve the noise immunity and
low-flowrate
sensitivity of the vortex flowmeter, great efforts have been
madeby a number of researchers. Kawano et al. [11] improved the
signal-to-noise ratio by using an adaptive low-signal-cutoff
discriminatorfunction. Amadi-Echedu et al. [12,13] applied signal
processingand system identification techniques to enhance
themeasurementquality of the vortex flowmeter. Pankanin and
Grzegorz [14]optimized the bluff body geometry and the sensor
location toimprove the frequency stability and the linearity of the
flowmetercharacteristic.Onemethod of improving low-flowrate
sensitivity and repeata-bility of the vortex flowmeter is to use
two bluff bodies in se-ries or tandem separated by a narrow gap.
Honda and YamasakiInstrumentation 19 (2008) 350357 351
Fig. 1. Rectangular bluff body combination, courtesy of Bentley
and Benson [19].
Fig. 2. Combination of rectangular and triangle bodies, courtesy
of Bentley andBenson [20].
[15] investigated the stability of the vortex shedding from
bluffbodies. Igarashi [1618] worked on the regularity of the
vortexshedding and the strength of the vortices from circular
cylinderbodies in a uniform flow. Bentley and Benson [19] examined
theperformance of a number of rectangular bluff body combinations
inexperiments. They found that the higher repeatability of
vortexshedding can be obtained with optimal dual bluff body
combina-tions. As shownas in Fig. 1, they tested combinations of
two rectan-gular bluff bodies in series and showed that certain
combinationsgave higher repeatability over a range of flow
conditions than an asingle rectangular bluff body. Bentley and
Benson then proposedthe condition for optimum vortex shedding in
combinations oftwo rectangular bluff bodies in tandem. In
particular, they showedthat the dual rectangular bluff body
combinations satisfyingcondition (A):
l1d= 0.500, L
d= 0.400, l2
d= 0.100, d
D= 0.1. (3)
A deeper rectangle upstream of a narrower rectangle gave
thehighest repeatability of all the combinations tested.This work
was then extended to combinations of rectangular,
triangular and chevron shaped bluff bodies in series [20]. Fig.
2shows a combination satisfying condition (A) but with
thedownstream rectangle replaced by a triangle again, which
yieldsthe highest repeatability of the combinations tested.Igarashi
et al. [21] measured the flow resistances of several
cylindrical vortex shedders under a turbulent flow
conditionthrough a circular pipe over a wide range of Reynolds
number andthe opening ratio.Igarashi [22] studied the performance
of a cylinder with a two-
dimensional slit along the diameter and a
triangular-semicylinderbody, shown in Fig. 3. They demonstrate that
a cylinder with atwo-dimensional slit along the diameter satisfies
condition: d/D =0.200.30 and L/d = 0.150.16, and a
triangular-semicylinderbody satisfies condition: d/D = 0.200.30 and
L/d = 0.150.16,generating strong and regular vortex
shedding.Recently, Bentley andBenson [23] investigated the
visualizationcharacteristic of vortex shedding in open channel flow
for a singlerectangle bluff body and two dual bluff body
combinations (one is
-
352 J. Peng et al. / Flow Measurement and
Fig. 3. Design structure courtesy of Igarashi [22].
Fig. 4. Schematic diagram of our flowmeter experimental
apparatus.
dual rectangle combination, and the other is an upstream
rectangleand a downstream triangle combination).However, most of
the previous efforts aimed on improving
low-flowrate sensitivity and repeatability of the vortex
flowmeterby using two bluff bodies in series or tandem separated by
anarrow gap, and they seldom mentioned about vortex sheddingof
upstream triangle and downstream triangle combinations inseries.
The shape of the bluff body is important to the extent thatit
determines the location of the separation point on the rear body.In
the case of a vortex meter, the typical shape of the bluff body
ofvortex shedding is a square, rectangle, T, triangle or trapezoid.
Thesharp-corner of the triangle cylinder on vortex shedding
producesthe maximum disturbance in the bluff body, and is therefore
thebest design for a vortex meter. In industries, the most
currentlyapplied single vortex shedder is in the shape of a
triangle cylinder.Bentley and Benson [20] suggested that downstream
triangulardual bluff body combination gave the highest
repeatability of thecombinations. Then, the combinations of two
triangle bluff bodiesin series should be tested.Fuxin et al. [24]
investigated the hydrodynamic vibration
characteristic of dual triangle-section bluff body combinations
inseries by numerical simulation. They suggested that dual
triangle-section bluff bodies combinations in series can increase
the SNRof vortex flowmeter and reduce flux lower limit value of
vortexflowmeter.This paper presents results from a flowmeter
experimental
apparatus. In experiments,we applied a number of dual
triangulatebluff body combinations in a circular pipe, and tested
the vortexshedding performance of these different size and
geometries bodycombinations. Finally, those experimental results
are discussed indetail, and some implications are revealed on the
design of dualtriangulates.
2. Experimental apparatus and procedure
Our experiments were performed in a flowmeter
experimentalapparatus, and Fig. 4 shows its schematic diagram.
Basically, theflowmeter experimental apparatus is composed of five
parts.Part I is a straight circular pipe with an inner diameter of
D =
50 mm and a length of L0 = 5 m, which is located on 100D
down-
stream from the inlet of the pipe. Flow is conditioned by this
up-streamof test section. Flow through the test section presents a
fullyInstrumentation 19 (2008) 350357
Table 1Shape and dimension of bluff body
developed turbulent. A mean uniformity of the flow is less
than3% and a free stream turbulence intensity of that is less than
0.7%over a velocity range of 260m/s.Part II is the tested
flowmeter. In order to optimize the test
number, through an orthogonal collocation method, nine pairs
ofdual triangulate bluff body combinations in different sizes
andseparations ranging from 40 to 65 mm are used in the
presentstudy. Table 1 lists the geometry and parameters of the
bluffbodies. Table 2 names the test number for the different dual
bluffbody combinations. In an extended program of work, we
havemeasured the performance of a wide variety of combinations
oftwo triangulate bluff bodies in series. This program has
shownthat for any combination geometry the most regular shedding
isobtained if the separations distance L is larger than 40 mm. IfL
< 40mm, themost regular shedding cannot be obtained. It couldbe
partly explained by the location of the second separation pointon
the after body. In the two triangulate bluff bodies in series,
thereare two flow separations. The first flow separation is
produced bythe first separation point on the before body and the
second one isproduced by the second separation point on the after
body. Lmayinfluence the location of the separation point on the
after body.Part III is a standard flow device. It is composed of a
seven-
nozzle flowmeter and the variation of flowrate can be obtained
bythe different nozzle combinations. The experimental volume flowis
the calculation flow of the nozzle flowmeter. The uncertaintyof the
volume of the nozzle flowmeter is 0.5%. To clarify theReynolds
number effect on the flow characteristics, the meanvelocity Um was
set over a range of 260 m/s. The mean velocityUm was specified by
Q/(piD2/4), where Q is the volume flowrate measured by the nozzle
flowmeter. Those flow velocitiescorrespond to the Reynolds number
of the pipe, Re = UmD/, witha range of 6.62 1031.99 105.Part IV is
a vacuum pump, which is used to generate a pressure
gradient in the experiments.Part V is the computer measurement
system. It is composed of
a charge amplifier, multi-channel dynamic analyzer and
computer.The sensor signals are amplified by the charge amplifier,
andare then transmitted to the computer through the
multichanneldynamic analyzer.
The vortex shedding frequency is obtained from the measured
fluctuating pressure by piezoelectric press sensors. The two
-
cfrequency characteristic of a single bluff body. A plot of
Strouhalnumber vs. Reynolds number and mean velocity for the five
bluffbodies studied is shown in Fig. 6. For a given bluff body,
theStrouhal number is maintained constant over the entire
Reynoldsnumber range tested. Table 3 shows its mean value and error
forthe five bluff bodies studied.The linearity of the Strouhal
number is evaluated quantitatively
by the error , which is defined as:
= 1N
Ni=1
(Si S /S) (5)where S is themean value of the Strouhal number, Si
is the Strouhalnumber of the ith Um, N is the number of test
Um.
results of for a commercial vortex flowmeter were shown tohave a
value of as 0.79%1% (4 m/s < Um < 20 m/s,D =150 mm, mean
value of S as 0.250.26) by Igarashi [22]. Theuncertainty in the
error of the Strouhal number results mainlycomes from the
uncertainty in flowmeter experimental apparatus.The base error of
flowmeter experimental apparatus is 0.5%. Ifthinking the base error
of the flowmeter experimental apparatus,the error of No. 4 bluff
body is about 0.806%. Therefore, No. 4bluff body is chosen as the
reference for comparison in theexperiment.
4. Experimental results and discussion
In order to achieve the sufficiently high SNR by a
piezoelectricJ. Peng et al. / Flow Measurement and
Table 2Dual bluff body number
Dual bluff bodynumber
First bluff bodynumber
Second bluff bodynumber
Blo
1 4 4 332 5 8 363 3 1 384 6 7 335 9 2 336 7 3 367 2 5 388 8 6
369 1 9 38Reference for comparison in experiment 33
Fig. 5. Fluctuating pressure and its power spectrum.
piezoelectric sensors were symmetrically stuck on the lateral
sideof the second bluff body as shown in Table 1. The blockage
ratio Scis defined by the projected area of the model over the test
section.In this paper,
SC = (D d1)/(piD2
4
). (4)
3. Reference for comparison in experiment
Fig. 5 shows typical results in the case of a circular pipe.
Thespecified frequency is equal to the vortex shedding frequency f
.In order to establish a reference for comparison, approach
velocity and shedding frequency were measured for a single
bluffbody over a velocity range of 460 m/s. Using air as the
workingfluid and the bluff body wide range of 1315 mm, the
Reynoldsnumber varied in the range of 1.32 1041.99 105. In orderto
optimize the test number, we choose five single bluff bodies(No. 2,
No. 4, No. 5, No. 6, and No. 7) to study the vortex sheddingIn Fig.
6, the Strouhal number is affected by the b and d ofthe bluff body,
and Um as well. Results of Strouhal number for aInstrumentation 19
(2008) 350357 353
kage ratio Sc (%) Characteristic of dual bluffbody
d1/D d2/D b1/D b2/D
d1 = d20.26 0.26 0.34 0.340.28 0.28 0.44 0.400.30 0.30 0.40
0.42
d1 < d20.26 0.28 0.36 0.380.26 0.30 0.38 0.440.28 0.30 0.38
0.40
d1 > d20.30 0.28 0.44 0.380.28 0.26 0.40 0.360.30 0.26 0.42
0.38
N0.4 bluff body
Fig. 6. Strouhal number of single bluff body.
Table 3Strouhal number error of single bluff body
Bluff body number S (%) Umin (m/s)
No. 2 0.25627 0. 636 4No. 7 0.27407 0. 88 4No. 6 0.26049 0. 536
4No. 5 0.28429 0. 386 4No. 4 0.26403 0. 306 4
commercial vortex flowmeterwas shown to have amean value of Sas
0.250.26 by Igarashi [22]. The reason of the variations, decreaseor
increase in Fig. 6 could be explained by blockage effect and
thedifferent value of d parameter used in the calculation of the S
[25].In Table 3, the error is affected by b and d of the bluff
body.
Among them, the value of No. 4 bluff body is minimal.
However,press sensor for the single bluff body in the lower
Reynoldsnumber, we have measured the performance of the single
bluff
-
(a) No. 1 bluff body combination. (b) No. 2 bluff body
combination.
(c) No. 3 bluff body combination. (d) No. 4 bluff body
combination.
(e) No. 5 bluff body combination. (f) No. 6 bluff body
combination.
Fig. 7. Strouhal number of dual bluff bodies and the deviation
values (the error ) for fitted SUm curves.
body in an extended program of work. This program has shownthat
the most regular shedding is obtained if the mean free-stream
velocity (Um) is larger than 4 m/s for the single bluff
Then, we have measured the performance of combinations of
twotriangulate bluff bodies in series. This program has shown
thatthe most regular shedding could be obtained if Um < 4 m/s
for354 J. Peng et al. / Flow Measurement andbody. If Um < 4 m/s,
the most regular shedding cannot beobtained by a piezoelectric
press sensor for the single bluff body.Instrumentation 19 (2008)
350357combinations of two triangulate bluff bodies in series. When
Um =2m/s, themost regular shedding can be obtained by a
piezoelectric
-
(i) No. 9 bluff body combination.
Fig. 7. (continued)
press sensor for combinations of two triangulate bluff bodies
inseries. Therefore, using the combinations of two triangulate
bluffbodies in series can improve the low-flowrate sensitivity of
thevortex flowmeter.In our work, we chose 15, 20, 25, 50, 100, 150,
200, 250, 300,
350 and 400 m3/h as the experimental volumes flow. So
theexperimental flow velocities are 2.1, 2.8, 3.5, 7.1, 14.2, 21.2,
28.3,35.4, 42.5, 49.5 and56.6m/s, respectively. Those experimental
flowvelocities gradually increase from 2 to 60 m/s. In the
experiments,each of the tests for different arrangement are
repeated 5 times.The repeatability of each velocity is less than
0.4%.The correlations of vortex shedding Strouhal number (S) of
nine
bluff body combination vs. mean velocity and Re are shown inFig.
7, together with the deviation values (the error ) for fittedSUm
curves.Shown in Fig. 7, for those vortex shedders, this linearity
of
different bluff body combination has a noticeable difference.
Thevortex shedding Strouhal number varies with its shape and the
slitlength L. The Strouhal number of those bluff body
combinationsis generally smaller than that of the single bluff
body. In someconditions, the Strouhal number of No. 3, 5 and 6
bluff bodycombinations is larger than that of the single bluff
body. Thereason of higher or lower Strouhal number for the two
bluff body
could be partly explained by the location of the separation
pointon the different after body. In the above interpretation, for
the twotriangulate bluff bodies in series, there are two flow
separations.The first flow separation is produced by the first
separation pointon the before body and the second one is produced
by the secondseparation point on the after body. The location of
the separationpoint on the different after bodymay influence the
vortex sheddingfrequency (f ) value of the bluff body
combination.In order to help analyze the Strouhal number of those
bluff body
combinations, we categorize them into three types based on
therelationship between d1 and d2. The characteristic of type I,
II, andIII combinations are d1 = d2, d1 < d2, and d1 > d2,
respectively.From Table 2, No. 1, 2 and 3 bluff body combinations
are type Icombination, 4, 5 and 6 are type II combination, and 7, 8
and 9 aretype III combination.From Ref. [5], the distance between
consecutive vortices is
4pid/3 (about 4.2d) and invariant, which is confirmed by
exper-iment. l = 4.2d is defined as the distance between
consecutivevortices. L is defined as opening length of two bluff
bodies. The re-lationship between l and L is evaluated
quantitatively by K , whichis defined as:
K = L/l. (6)J. Peng et al. / Flow Measurement and
(g) No. 7 bluff body combination.combinations than the single
bluff body is the different vortexshedding frequency (f ) value of
the bluff body combination. ItInstrumentation 19 (2008) 350357
355
(h) No. 8 bluff body combination.The linearity of the Strouhal
number is evaluated quantitatively bythe error from Eq. (5). The
Strouhal numbers of dual triangulate
-
356 J. Peng et al. / Flow Measurement and
Fig. 8. Strouhal number error of type I combination.
Fig. 9. Strouhal number error type II combination.
Fig. 10. Strouhal number error type III combination.
bluff body combinations for Um are in range of 260 m/s and
thatof a single bluff for Um is in range of 460 m/s.The
correlations of vortex shedding Strouhal number error ()
of dual triangulate bluff body combinations and a single bluff
bodyvs. K are shown in Figs. 810. Fig. 8 presents the
comparisonbetween the Strouhal number of type I combination and a
singlebluff body. The error for type I is larger than that of the
single bluffbody and is affected by K , which can be optimized. For
example,when K 1, d1/D = d2/D = 0.26 and b1/D = b2/D = 0.34,the
error of No. 1 dual triangulate bluff body is the same as thatof a
single bluff body. Fig. 9 presents the comparison between the
Strouhal number of type II combination and a single bluff
body.The error for type II is larger than that of the single bluff
bodyInstrumentation 19 (2008) 350357
and is affected by K . As K increases, decreases. When K 1, is
minimum. However, the minimal for type II is larger than thatof a
single bluff body. Fig. 10 presents the comparison between
theStrouhal number of type III combination and a single bluff
body.The error for type III is larger than that of the single bluff
bodyand is affected by K , and it reaches a minimum for K in the
rangebetween 0.7 and 0.85. However, the minimal for type III is
largerthan that of a single bluff body.From Figs. 8 to 10, we
observed sudden decreases in errors from
L = 40 to 45 mm (K 0.60.75). In the above interpretation, Lmay
influence the location of the separation point on the
differentafter body. For a dual triangulate bluff body, the width
of theopening length corresponds to L = 40 mm (K 0.6) is a
criticalvalue. When L > 40 mm (K > 0.6), the most regular
sheddingis obtained. If L < 40 mm (K < 0.6), the most regular
sheddingcannot be obtained. Therefore, there are sudden decreases
in errorsfrom L = 40 to 45 mm (K 0.60.75).
5. Conclusions
We investigated the Strouhal number for flow past
dualtriangulate bluff bodies. Our work can be summarized as
follows;
(1) using the combinations of two triangulate bluff bodies
inseries can improve the low-flowrate sensitivity of the
vortexflowmeter.
(2) The linearity of the Strouhal number of dual triangulate
bluffbody combinations varies with opening length L and d1 and
d2.The best linearity of the Strouhal number of dual
triangulatebluff body combinations is the same as that of a single
bluffbody.
(3) The optimal dual triangulate bluff body diameter
correspondsto d1 = d2 = 13 mm (d/D = 0.26). In order to generate
themaximum disturbance in the bluff body and the most
regularshedding, the optimal height of a dual triangulate bluff
body is0.34D i.e. 1.3d (b 0.34D).
(4) For a dual triangulate bluff body, the optimal opening
lengthof two bluff bodies corresponds to K 1. In those cases,
thestrong vortex generates and regular vortex shedding occurs.
(5) The design criterion of the dual triangulate bluff body
vortexflowmeter was advanced in the following. If the pipe
diameteris D, then d1 = d2 = 0.26D, b1 = b2 = 0.34D and
openinglength of two bluff bodies (L) is equal to the distance
betweenconsecutive vortices of flow over single bluff body (l =
4.2d),i.e. K 1. It will be valuable in the flow measurement
andinstrument design of vortex flowmeters in industries.
Acknowledgements
This project is supported in part by the National HighTechnology
Research and Development Program (863 Program),the Key Technology
of Oscillatory Type Flowmeter (Grants No.2002AA423180), and the
National Science Foundation Project, Thecontrol theory and method
of representative exciting flow field inhydraulic component (Grants
No. 59835160), from the governmentof the Peoples Republic of
China.
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Experimental investigations of Strouhal number for flows past
dual triangulate bluff bodiesIntroduction and
backgroundExperimental apparatus and procedureReference for
comparison in experimentExperimental results and
discussionConclusionsAcknowledgementsReferences