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: pengjiegang@uestc.edu.cn, pjg2000cn@163.com (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