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Sensors and Actuators A 170 (2011) 8– 23

Contents lists available at ScienceDirect

Sensors and Actuators A: Physical

j ourna l h o me pa ge: www.elsev ier .com/ locate /sna

eview

eview on vortex flowmeter—Designer perspective

. Venugopal, Amit Agrawal, S.V. Prabhu ∗

epartment of Mechanical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India

r t i c l e i n f o

rticle history:

a b s t r a c t

This paper highlights various aspects of design of a vortex flowmeter. Vortex shedding and vortex flowme-

eceived 1 February 2011eceived in revised form 6 May 2011ccepted 31 May 2011vailable online 7 June 2011

eywords:

ters are known from decades. However, the vortex shedding phenomenon is not understood clearly asapplicable to vortex flowmeter. In the recent past large body of literature is reported on the perfor-mance of vortex flowmeter. This report comprehensively summarizes all the improvements which helpthe designer to build a vortex flowmeter. The paper systematically explains various aspects related todevelopment of a vortex flowmeter with peculiarities associated with its design.

© 2011 Elsevier B.V. All rights reserved.

ortex shedding, Vortex shedder

ontents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82. Evolution of vortex flowmeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93. Design of vortex flowmeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1. Primary element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2. Secondary element (sensor) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2.1. Force/torque/stress detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2.2. Ultrasonic measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2.3. Differential pressure measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4. Flow field investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.1. Flow visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.2. Hot wire measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.3. Modern computers and vortex flowmeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5. Installation effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146. Signal processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177. Measurement uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198. Vortex flowmeters and two phase flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Biographies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

. Introduction

Energy prices have surged upward leading to increased demandor precise flow measurement. The IEO2010 reference case sug-ests that liquid fuels, coal and natural gas are the largest source of

custody transfer but also in other sectors like energy conservationand human comfort. The CO2 emissions are expected to increaseby 14% from 2007 to 2020 [1]. In the recent past, energy con-servation steps are being implemented in the industries to cutdown CO2 emission and to earn carbon credits. This essentially

nergy worldwide. The industrial sector and transportation sec-or consumes about 50% and 30% of the world’s total deliverednergy, most of it in the form of liquid fuels. Fluid flow mea-urement in industrial sector holds great importance not only for

∗ Corresponding author. Tel.: +91 22 2576 7515; fax: +91 22 2572 6875/3480.E-mail addresses: svprabhu@me.iitb.ac.in, svprabhu@iitb.ac.in (S.V. Prabhu).

924-4247/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.sna.2011.05.034

requires continuous and detailed monitoring of process fluids ateach and every consumption point. Energy audits in thermal sec-tors are always accomplished with precise flow measurements. InEuropean countries district heating is another growing area where

precise metering of steam is required. In district heating, central-ized heating system is provided for a group of houses. Natural gasis main source of energy in domestic sector in European countries.Domestic users are understandably concerned about their steam

A. Venugopal et al. / Sensors and A

Nomenclature

A cross sectional area of pipe (m2)b length of the triangular bluff body (m)

C ′p pressure loss coefficient (C ′

p = (p′ )0.5

/0.5�U2m)

D diameter of pipe (m)D̄ mean diameter of ring (m)Do outer diameter of ring (m)Di inner diameter of ring (m)d width of bluff body (m)e wake width (m)f vortex shedding frequency (Hz)fp frequency of unsteady flow (Hz)fi mean vortex shedding frequency (Hz)G gap width between the outer edge of the ring and

pipe wall (m)g distance between two vortices (m)KL pressure loss coefficientK K-factor K = St/A × d (Hz/m3/s)Kmin minimum K-factorKmax maximum K-factorKmean mean K-factorL vortex shedder body length (m)P0 power of the vortex shedding frequency component

(W)Pi power of the other component contained in the

interval i (W)Pt total energy of the spectrum (J)P’ fluctuating component of pressure (Pa)P(w) energy content in frequency component (J)s slit (m)Um mean velocity (m/s)Ur reduced velocity (Ur = Um/(fp × d))we upper bound frequency in the spectrum (Hz)W thickness of the ring (m)X streamwise coordinate (m)

Non-dimensional numbersReD Reynolds number (�UmD/�)Red Reynolds number (�Umd/�)St Strouhal number (St = fd/Um)

Greek symbols� Fluid density (kg/m3)� Dynamic viscosity (Pa s)� von Karman constant (m2/s2)

2 3

aicha

titaaflmmfl

the diffusion length. Bearman [7] suggested that lateral distance

ε rate of dissipation of � (m /s )

nd gas metering bills. Due to large volumes, small inaccuraciesn measurement may have serious financial implications at bothustomer and supplier end. In the recent past, water managementas become another major challenge. These examples suggest thatccurate flow measurement is relevant and essential.

The world wide flowmeters can be divided into two parts, theraditional and new technology. The traditional technology mainlyncludes differential pressure devices. The performance of new-echnology flowmeters is typically at a higher level for criteria suchs accuracy and long time reliability with minimum maintenances compared to traditional technology meters. New-technologyowmeters include Coriolis, magnetic, vortex, ultrasonic and ther-

al. The top three new-technology flowmeters used in the energyarkets are Coriolis, ultrasonic and vortex. The advantage of vortex

owmeter over Coriolis and ultrasonic is low cost and low mainte-

ctuators A 170 (2011) 8– 23 9

nance. The vortex flowmeter is not sensitive to physical propertiesof the fluid like density and viscosity which makes them versa-tile, the same meter can be used in any medium. The calibrationof the meter performed in one medium, can be used for any othermedium. This is not the case for Coriolis and ultrasonic meters.Over and above that the operating temperature and pressure rangefor vortex flowmeters are very large (−40 ◦C to 400 ◦C and 30 bargauge). Some chemical industries use high pressure nitrogen toclean their system. Vortex flowmeters are the best choice for suchapplication where turbine meter and positive displacement metersare susceptible to mechanical damage. The accuracy and reliabilityof vortex flowmeters keeps them ahead of differential pressure flowmeasurement devices. The typical accuracy and turn-down (oper-ating range) clams for vortex flowmeters are ±0.5–1% of the readingand 1:14 [2]. Compared to differential pressure devices, they offerthree times lower permanent pressure loss and good repeatability(0.1–0.2%).

Vortex flowmeters play a major role worldwide in flow mea-surement business. From the last three decades, vortex flowmetersare extensively used in industries. The vortex flowmeter is beingcurrently applied extensively in the measurement of liquids, gasesand steam over a wide range of flow rates. In enhance oil recoverysystem vortex flowmeters are used to measure carbon dioxide. Insemiconductor industries vortex flowmeters are used to preciselymeasure ultrapure water for etching process. Highly corrosive acidslike ferric chloride, hydrochloric acid, and sodium hydroxide arealso metered using vortex flowmeter in waste water treatmentplant. The vortex flowmeter is finding its applications in manysectors and is in direct competition with Coriolis and ultrasonicflowmeters, where cost is a constraint.

Pankanin [3] reviewed fundamental aspects related to vortexflowmeter design. However, the descriptions are comprehensiveand detailed information is lacking. This paper is written from theperspective of designer of vortex flowmeter. The optimum vortexshedder shapes, sensing technologies, installation effects, uncer-tainties and signal processing aspects are covered in detail andsummarized. This helps a designer to build a vortex flowmeter onthe basis of available literature.

2. Evolution of vortex flowmeters

The vortex flowmeter is a device that works on the principleof shedding of vortices behind a bluff body placed in the flow. Inthe fifteenth century the great Italian painter Leonardo da Vincidescribed and drew accurately the vortices behind cylindrical body.Later in 1878 Strouhal based on his observation published a relationfor the vortex shedding frequency. This relation later representedin dimensionless form as:

St = fd

Um(2.1)

The first theoretical investigation on this subject was reported in1911. Von Karman derived the geometrical pattern of the vorticesbehind a circular cylinder based on linear stability analysis. He alsoestablished a theoretical link between the vortex street structureand drag experienced by the body. In the early stage there was a lotof discrepancy in the literature related to the choice of appropri-ate characteristic length for defining the non dimensional Strouhalnumber. Roshko [4] defined non dimensional Strouhal numberbased on wake width. Goldburg et al. [5] defined Strouhal numberbased on the total wake momentum thickness. Gerrard [6] definedtwo Strouhal number based on length of the formation region and

between two vortices is the appropriate length scale. Roshko [8]was the first who suggested designing a flowmeter based on thenon dimensional Strouhal number (based on cylinder diameter).

10 A. Venugopal et al. / Sensors and Actuators A 170 (2011) 8– 23

TRmc

soeeaaaTttcpS

sdtgcigr

3

tpcwrolmtmmfHrsCRci

Fig. 1. Vortex shedding characteristic lengths.

he basis ideal was to use the linearity of Strouhal number witheynolds number as constant and calculate the flow velocity byeasuring the vortex frequency. He studied vortex shedding from

ircular cylinder in a Reynolds number range ReD = 4 × 105.Gerrard [6] first explained the physical insight in to the vortex

hedding mechanism. The forming vortex draws the shear layer ofpposite sign from the other side of the wake centre line, whichventually cuts off the supply of vorticity to the growing vortex. Hexplained that the constancy of Strouhal number results from a bal-nce between two length scales in the near wake: formation lengthnd diffusion length. The universal Strouhal number is now usu-lly defined based on bluff body width as the characteristic length.he vortex shedder width is a convenient engineering parametero measure with minimal uncertainties. The major problem withhe other above mentioned characteristic length scales was diffi-ulty in physical measurement and generalization on to a commonlatform. The various characteristic lengths used for defining thetrouhal number are shown in Fig. 1.

It is interesting to note that the basic principle of vortexhedding technique was established in early 1970s. It remainedormant until modern materials and electronics provided a routeo commercial realisation by detecting and amplifying the signalenerated by the shedding process. By early 1990s many commer-ial manufacturers came up with vortex flowmeters with modernnstrumentations and the market for the vortex flowmeters startedrowing rapidly due to high accuracy, turn-down ratio and goodepeatability.

. Design of vortex flowmeter

The industrial user is rather conservative in selecting a flowme-er for a specific application. An inappropriate decision may lead torocess shut down, loss of output, process inefficiency or hazardousonditions. The desirable characteristics of a good flowmeter are:ide dynamic range of measurement, wide operating temperature

ange, insensitivity to swirl, flow profile distortion, viscosity andther physical properties of the fluid, small irrecoverable pressureoss, fluid versatility, immunity to vibration and other electrical and

agnetic interferences, availability in all practical sizes, immunityo pulsating flow effects, accurate and low cost to purchase and

aintenance. A vortex flow meter possesses majority of the aboveentioned characteristics. In principle, the Reynolds number range

or vortex flowmeters with sharp edge bluff bodies is around 1:100.owever, in practice, vortex strength becomes weak at low flow

ates and detection of vortices becomes difficult by passive sen-ors. This restricts the lower end of the Reynolds number range.

avitations in liquids and compressibility effects in gases limit theeynolds number at the upper end. Typical operating range forommercial vortex flowmeter for air is 6–80 m/s and for water its 0.3–9 m/s. The typical accuracy claims are ±1–1.5% for gases and

Fig. 2. Block diagram of a typical vortex flowmeter.

steam and ±0.85% for water [2]. The lower limit on the Reynoldsnumber is 20000. However, some manufacturers claim that thedevice can be used below the above mentioned Reynolds numberwith reduced accuracy.

The overall working methodology of the vortex flow meterinvolves the detection of the vortex strength and frequency by anappropriate sensor. Detected signal is analysed in the front endelectronics to measure the energy content and frequency of thevortices. The signal convertor converts this signal into some stan-dard analogue output (usually 4–20 mA). The analogue output canbe displayed locally or can be transmitted by any protocols likeFieldbus, Modbus etc. for further analysis. The vortex flowmetercomprises two parts namely primary element and secondary ele-ment as shown in Fig. 2.

3.1. Primary element

The primary element is the vortex shedder with pipe assem-bly and sensor. The heart of the flowmeter is the vortex shedder.The strength, linearity and stability of the vortex are defined bythe shape, blockage and other geometrical parameters of the vor-tex shedder. The rangebility of a flowmeter is primarily definedby the vortex shedder. Conventional vortex flowmeters are avail-able in various pipe diameters ranging from 0.5 inch to 12 inch.Limitations on the manufacturing tolerances and engineering chal-lenges put limits on lower sizes. However, a diameter above 12inch makes this product uneconomical. The first commercial vortexflowmeter for closed conduit pipe was manufactured by Yokogawain 1968 to measure flare stack and flue gas flow rates. In the earlystages, most of the manufacturers used circular cylinder as thevortex shedder. This led to various problems like stability of thevortices and rangebility. Achenbach [9] experimentally measuredlocal pressure and skin friction around a circular cylinder in sub-critical Reynolds number region (Red = 6 × 104–3 × 105). His workhighlighted that the flow separation point is not fixed for the entirerange of the Reynolds number. The linearity of Strouhal numberrequires the location of the separation point to be fixed irrespec-tive of Reynolds number. The ideal bluff body should have sharpedges at the point of flow separation to avoid Reynolds numbereffect due to shift in separation point. This puts limitation on cir-cular cylinder as a vortex shedder for flow metering application.The variation of Strouhal number with Reynolds number for dif-ferent vortex shedder configurations collated from various sourcesis summarized in Fig. 3. The figure shows that the operating rangefor vortex flowmeters is very large (1:100). The scatter in Strouhalnumber values is mainly because of different geometrical shapesof the vortex shedders used.

The effect of body length of the vortex shedder can be explainedby Gerrard [6] analogy of splitter plate. The presence of splitterplate increases the thickness and diffusion of the shear layers.This ensures high spread of circulation at the end of the forma-

A. Venugopal et al. / Sensors and A

141210860.1200

0.1600

0.2000

0.2400

0.2800

0.3200

St

12000002200 0005

Re D

Igarashi [2 4] Miau et al. [20] Zhang et al. [35] Peng et al. [26] Venug opal et al. [37 ] Takamoto et al. [60]

ttqaos

rPapBtsthlswiliv

F

ln(ReD)

Fig. 3. Strouhal number variations with Reynolds number.

ion region. All the above mentioned effects cumulatively increasehe time for vortex shedding and hence reduction in shedding fre-uency. The interference of oppositely signed vorticity also reducesnd hence the strength of growing vortex increases. The lengthf the after body should be sufficiently large to stabilize vortexhedding.

Flow around circular cylinder under low blockage ratio iseviewed by various researchers (Norberg [10], Mustafa et al. [11],rasad et al. [12] and Yokuda et al. [13]). Circular cylinder is notn attractive shedder from viewpoint of vortex shedding. Thisaper rather focuses on papers relevant to vortex flowmeter design.lockage ratio is highly influencing parameter in the design of vor-ex flowmeter. The blockage ratio is defined as the ratio of vortexhedder width to the pipe diameter. High blockage ratio may leado the interaction of the vortices with the pipe walls, which willamper the vortex shedding mechanism. On the other hand, too

ow blockages put limitation on signal detection due to poor vortextrength and are therefore avoided. The Strouhal number variationith blockage ratio for trapezoidal bluff body is linear as shown

n Fig. 4. Awbi [14] based on his experimental observations, high-ighted that the Strouhal number for two dimensional bluff bodiesn presence of blockage is linearly dependent on the shear layerelocity parameter.

0.400.300.200.10Blockage

0.120

0.160

0.200

0.240

0.280

0.320

St

Takamoto [60] Venugopal et al .[37]

ig. 4. Strouhal number variations with blockage ratio for trapezoidal bluff body.

ctuators A 170 (2011) 8– 23 11

Wahed et al. [15] studied various sharp edge bluff bodies likecylinder, rectangle, trapezoid and T-shaped body. They concludedthat the T- shaped body is the most appropriate shape. Miau et al.[16] and [17] suggested axisymmetric ring shaped bluff bodies forvortex flowmeter application. The advantage of ring shaped bod-ies is low irrecoverable pressure loss compared to conventionaltwo dimensional bluff bodies. The experimental investigations ofCousins et al. [18] pointed out certain interesting features of ringshaped bluff body vortex dynamics. In the ring shaped bluff bodiestwo different sets of vortices are shed from the outer and the innerring. The outer ring vortices travel slower than the inner ones due tothe influence of the pipe wall. The outer ring vortices decay morerapidly than the inner ones. Hence, it was desirable to measureinner vortices to get good estimate of vortex frequency. However,the strength of the inner vortices was very small to be capturedby passive devices like piezoelectric, strain gauge and differentialpressure sensors. Coulthard et al. [19] experimentally investigatedthe performance of two T-shaped and one trapezoidal vortex shed-der and concluded that T-shaped shedder is the best in terms oflinearity. Miau et al. [20] used a trapezoidal T-shaped body as avortex shedder. The extended plate behind the bluff body plays avital role in stabilizing the vortex shedding, and hence improvesthe linearity. The optimum length of the extended plate was foundto be 1.56–2 times the width of the vortex shedder. Turner et al.[21] and Popiel et al. [22] suggested a new design of the bluff bodyas a cylinder with a slit with concave rear face as shown in Table 4.Lavante et al. [23] based on numerical simulations suggested a newdesign of vortex shedder with flat front face and a bulged rear facewithout any sharp edges. However the complete dimensions of thebluff body were not reported completely.

Igarashi [24] experimentally studied three different bluff bodies(trapezoidal, cylinder with slit and triangular semicircular cylin-der). The experiments are conducted with air as the workingmedium in ReD = 1.9 × 104–2.5 × 105. The most important outcomeof his work was circular cylinder with a slit as an improved vortexgenerator. A circular cylinder with a blockage ratio of 0.20–0.267and slit width to vortex shedder width s/d = 0.10 was the most effi-cient vortex shedder. The pressure loss coefficient of the circularcylinder with slit was 50% less than that for a trapezoidal vor-tex shedder for the same blockage ratio and the Reynolds numberrange.

The evolution of cylinder with slit as an improved vortex shed-der appears to have motivated various researchers to investigatedual bluff bodies for vortex flowmeter applications. Bentley [25]studied rectangular bluff bodies in tandem for vortex flowmeterapplication. The downstream bluff body with convex rear faceincreases the repeatability of the shedding vortices. Peng et al.[26] and [27] studied the influence of distance between (separa-tion length) dual triangular vortex shedders on the performanceof the vortex flowmeter. The Reynolds number range covered wasReD = 5.6 × 103–1.6 × 105. The most interesting observations of thisstudy: (1) the irrecoverable pressure loss for certain separationlength was less than that of single bluff bodies. (2) The minimummeasurable velocity for dual triangulate bluff body combinationwas half of that of the single bluff bodies. (3) The sensitivity ofmeasured signal was higher at lower velocities. Fu et al. [28] stud-ied dual triangulate bluff bodies and obtained the optimum ratio ofseparation length to length of bluff body as 2.5 to achieve maximumhydrodynamic vibrations. This suggests that dual vortex shed-der increases the sensitivity of the vortex flowmeter at low flowrates.

From the literature, it may be inferred that there is no universal

bluff body as such for vortex flowmeters. Any bluff body, whichfulfils the characteristics of an ideal vortex shedder, can be used.Most of the commercial vortex flowmeter manufacturers preservedtheir bluff body design by patent laws.

1 and A

3

rdcidaiprvvqiepfif

3

mbsitflobtdadmas

iot[vscbsirtifbss

3

iluvted

2 A. Venugopal et al. / Sensors

.2. Secondary element (sensor)

The mechanism of vortex shedding behind the bluff bodies givesise to periodicity in the flow. In principle, any sensor which canetect the periodic fluctuations in velocity, pressure or temperaturean be used to detect the vortex shedding frequency. The sens-ng technology can be classified into four categories: Force/Torqueetection, ultrasonic detection, differential pressure measurementnd measurement of temperature variations. The sensor acts as annterface to the electronics by feeding the vortex signal for furtherrocessing, to obtain the vortex shedding frequency. The dynamicange of vortex flowmeter in terms of vortex shedding frequency isery large. The typical maximum and minimum frequency range forortex flowmeter is 1 Hz and 4000 Hz, respectively. The lower fre-uencies are usually encountered in low velocity fluids like water

n larger diameter pipes. However, the maximum velocities arencountered in high velocity fluids like air in smaller diameteripes. The dynamic characteristics of the sensor should be suf-ciently large to take care of this large dynamic range of vortex

requencies.

.2.1. Force/torque/stress detectorsMost of the commercially available vortex flowmeters in the

arket use a piezoelectric crystal embedded either inside the bluffody or inside a mechanical structure placed behind the vortexhedder. Piezo sensors use piezo-electric elements to detect strainn some mechanical arrangement having sufficient area exposed tohe differential pressure of the vortices. These sensors detect theuctuating lift to measure the vortex shedding frequency. In casef sensors embedded on the bluff body, the bluff body needs toe arranged in a cantilever arrangement to get high deflection forhe piezo sensor. This design increases the chances of mechanicalamage as the natural frequency of the bluff body in cantileverrrangement is small and may coincide with the vortex shed-ing frequency. This may lead to resonance and hence may causeechanical damage. This type of design is not suitable for air, steam

nd other applications where the vortex shedding frequencies formaller diameter are higher (2000–4000 Hz).

The best method of using piezo sensors is to embed themnside a mechanical member and place the member downstreamf the shedder body. Most of the commercial manufacturers usehis method for detecting the vortex shedding frequency. Igarashi24] performed experiments with piezo sensors embedded insidearious vortex shedder bodies. However, details related to piezoensor type and embedment was not reported. Zheng et al. [29]onducted experimental studies with piezoelectric probe placedehind a trapezoidal bluff body. He found that the location of theensor behind the bluff body is crucial for obtaining good linear-ty in Strouhal number. The best location for the piezo sensor waseported to be half the wavelength of the vortex street. However,hese studies are restricted to open channel flows which do notnclude the influence of blockage. Peng et al. [26] and [27] per-ormed experiments in a circular pipe with piezo sensor placedehind dual triangulate bluff body. The optimum location of theensor was qualitatively reported as behind the separation point ofecond bluff body.

.2.2. Ultrasonic measurementUltrasonic sensors are active sensors. A beam of ultrasound

s sent across the pipe duct behind the bluff body. The receiverocated at the opposite side receives the signal and converts theltrasound back to electrical signal which is modulated to get the

ortex frequency. The biggest advantage of ultrasonic sensor is thathey are insensitive to pipe vibration. Coulthard [19] conductedxperiments with ultrasound transit time to measure vortex shed-ing from trapezoidal and T-shaped bluff bodies. Luna et al. [30]

ctuators A 170 (2011) 8– 23

used pulsed ratio frequency doppler ultrasound to measure vorticesbehind circular cylinder. Hans et al. [31,32] and [33] measured vor-tex shedding frequency behind triangular bluff body and observedthat ultrasound measurement is effected by the presence of sec-ondary vortices behind the trailing edge of the vortex shedder. Theultrasonic method of vortex detection is sensitive to the turbulentfluctuations associated with eddies and secondary vortices behindthe vortex shedder. This makes the extraction of vortex signal com-plex. This disadvantage makes ultrasonic vortex flowmeters leastpopular in industrial applications.

3.2.3. Differential pressure measurementIn differential pressure measurement the fluctuating compo-

nent of the differential pressure due to vortex formation is inferredto compute the vortex shedding frequency. The differential pres-sure measurement is a passive detection method. Here, the periodicdeflection of the sensing diaphragm caused by vortex differentialpressure is used to measure the frequency of the vortex shed-ding. The differential pressure sensor must possess high frequencyresponse, especially for high velocity fluid such as air. Miau et al.[16] observed that the vortex shedding behind bluff body in aclosed conduit results in unsteady flow behaviour near the wall.The unsteady behaviour can be picked up by a pressure sensormounted on the pipe wall. The biggest advantage of this methodis low vibration sensitivity. Axisymmetric circular rings were usedas vortex shedders in his experiments. Miau et al. [17] and [34]further explored various shapes of the ring for vortex flowmeterapplication. However, the optimum dimensions were not reported.The results were presented in non-dimensional form and thebest linearity in Strouhal number was observed for X/W = 2.25to 2.84 for rings having geometrical parameter in the range of5.03 < D/W < 10.63 and 0.5 < G/W < 0.53. Miau et al. [20] suggesteddrilling two taps on the face of the bluff body (T-shaped shed-der) behind the separation point for dynamic differential pressuremeasurement shown in Table 4.

Zhang et al. [35] used a modified approach for measuringthe vortex shedding frequency. Instead of using one pressure forobtaining the vortex shedding frequency, duct wall differentialpressure with two pressure measurements, one on the upstreamof the bluff body and the other downstream. The biggest advantageof this method is direct mass flow measurement. The magni-tude of the differential pressure signal and fluctuating componentswere used together to calculate the mass flow rate directly. Theexperiments conducted with equilateral triangular bluff body inair and water, showed good agreement with the results obtainedfrom piezoelectric sensor. The optimum location of upstream anddownstream taps reported was 1D and 0.2D, respectively. The min-imum Reynolds number covered in the present experiments wasReD = 30,000. Sun et al. [36] used a modified duct wall differentialpressure method with both the pressure taps located axisymmet-rically behind the bluff body. The vortex shedding takes placealternately from the sides of the bluff body, which makes the pres-sure signal obtained from both pressure taps 180◦ out of phaseand improves the strength of the signal. The advantage of thisdifferential arrangement was cancellation of common mode hydro-dynamic and other noises. This inherent characteristic makes themeasurement more reliable than conventional methods. The effectof connecting tubes however, plays an important role in the detec-tion of vortex signal at low flow rates due to dampening of thesignal. Sun et al. [36] conducted systematic sets of experiments tostudy the effect of sampling tube dimensions on the pressure sig-nal amplitudes. The results suggest using short and small diameter

tubes.

Venugopal et al. [37] explored duct wall differential pressuremethod in detail and investigated the influence of shape of thebluff body. A direct comparison of axisymmetric tap combination

and Actuators A 170 (2011) 8– 23 13

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ith differential taps revealed that axisymmetric tap combina-ion gives better results in terms of signal amplitudes. Variouswo dimensional bluff bodies (cylinder, triangle and trapezoid) andxisymmetric bluff bodies (rings and cones) were investigated. Theesults highlighted that trapezoidal bluff body was the most appro-riate bluff body for duct wall differential pressure method. In casef axisymmetric bluff body, the signal amplitudes were very lowaking detection of dominant frequency difficult. The effect of

lockage was also explored for equilateral triangular bluff bodies.lockage ratio of 0.30 was found out to be the best among three0.14, 0.24 and 0.30) different blockages studied. The optimal tapocation for the various blockages investigated was found out toe 0.714 times the diameter of the pipe times the blockage. Venu-opal et al. [38] studied blockage effects for trapezoidal bluff bodyith axisymmetric tap location. The optimum blockage ratio and

he non-dimensional tap locations were 0.28 and 0.714 times theiameter of the pipe times the blockage, respectively.

The above described methods are widely used for vortexowmeter application. However, there are some unconventionalethods for detection of vortex shedding frequency. Michiyoshi

t al. [39] used sheathed alumel-chormel thermocouple placedehind a cylindrical vortex shedder to compute the vortex sheddingrequency. Sproston et al. [40] developed an electrostatic device for

easurement of vortex shedding frequency. Itoh et al. [41] sug-ested direct measurement of mass flow rate by measuring theagnitude and frequency of lift force on the vortex shedder caused

ue to periodic vortex shedding. Stress measurement principleas employed with electrostatic stress detectors. Bera et al. [42]escribed a microprocessor based inductive type pick-up to detecthe vortex shedding frequency. Lielibady et al. [43] used mono-

ode fibre based on interferometric technique to measure theortex shedding frequency. Herzog [44] used light intensity mod-lation caused by vortex differential pressure on multi mode opticbre to detect the vortex shedding frequency. The above mentionedechniques are not so far implemented in commercial product tohe best of authors knowledge. These methods can be investigatedn detail to prove long term reliability in hostile environment, highemperature applications, etc.

The comprehensive description of various measurement tech-iques shows that piezo sensors and differential wall pressureeasurement are the most promising. In spite of possessing

ertain features of good measurement capabilities, ultrasonic mea-urement technique has some disadvantages like complex signalrocessing and high cost because of which it has not become pop-lar in industrial applications.

. Flow field investigations

In the early stages of vortex flowmeter development most of themprovements in the design were based on trial and error approach.

ith the evolution of modern sophisticated techniques like highpeed flow visualization, hot wire based measurements and highpeed computations, the vortex dynamics behind sharp edged bluffodies are studied in sufficient details leading to useful qualitativend quantitative insights.

.1. Flow visualization

Flow visualization was the earliest method employed to studyhe vortex wakes. Miau et al. [17] employed dye visualization tech-iques to understand the vortex shedding mechanism with ring

haped bluff bodies. Flow visualization images revealed that theresence of the pipe wall affects the vortex shedding mechanismnd for blockage ratio above certain values, vortex shedding wasompletely inhibited. Unsteady flow separation was observed near

Fig. 5. Dye visualization image for formation of vortex (Popiel et al. [22]).

the wall due to the entrainment effect from the shedding vortices.This leads to high unsteady pressure fluctuations near the walland hence formed the basis for vortex frequency measurement onpipe wall. Miau et al. [20] studied the performance of T-shapedbluff body using dye visualization in water. The optimum ratio ofwidth of the vortex shedder and length of the extended plate wasexplained in line with Gerrard [6] splitter plate analogy. Turneret al. [21] suggested improved vortex generator as a cylinder withslit and concave rear face. The dye visualization based experimentsin water channel showed that the oscillating fluid flow throughthe slit stabilizes and increases the strength of the growing vortex.Popiel et al. [22] investigated circular cylinder with slit and con-cave rear face using dye visualization and found that the geometryis very sensitive to end wall effect leading to horse shoe vortex. Reg-ular vortex shedding was accomplished by the use of two end tailsfixed to the rear surface of the bluff body near the walls. The dyevisualization image showing vortex formation is shown in Fig. 5.

Bentley [45] studied dual rectangular bluff body combination inopen channel water flow rig. Based on the statistical distribution ofthe captured images mean and standard deviation in Strouhal num-ber was obtained. Although, the results are not much relevant forvortex flowmeter application due to the absence of blockage affects,the study highlighted physical insights in to the vortex sheddingmechanism of dual vortex shedders.

Pankanin et al. [46] based on flow visualization and imageprocessing techniques, highlighted very important aspect of con-vection velocity and stagnation region in the formation of cylinderwake. The stagnation region was clearly visible for circular cylin-der. However, for cylinder with a slit this stagnation region wasnot so evident. The stagnation region acts as an information chan-nel between the vortices in case of cylinder. However, in case ofcylinder with slit the majority of the stagnation region was in theslit and this slit acts as an information channel for vortex shedding.Pankanin et al. [47] proposed a phenomenological model for deter-mining the energy and the convection velocity of the vortices. Thetwo dimensional vortex shedding phenomenon was divided intothree zones: intense development zone, stabilizing zone and decayzone. The model suggests that the rotational energy of the vorticesis maximum at the end of intense development zone. Pankanin et al.[48] proposed a modified numerical model for vortex street sim-ulation. The modified model takes into account the movement ofthe stagnation region over the shedding cycle, which was assumedstationary in the earlier model.

The important contributions of flow visualization are increasein stability and strength of vortices with improved vortex shed-ders. The purpose of introducing an optimum gap between dual

bluff bodies was to allow small quantity of flow through the gapto ensure clean detachment of the vortices and hence good linear-ity in Strouhal number. In case of dual bluff bodies, the upstream

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ody acts as a primary vortex generator and the secondary as anmplifier.

.2. Hot wire measurements

Hot wire probes played a significant role in the investigationsf best location of the senor to obtain stable and high amplitudeignals. Cousins et al. [18] investigated the signal to noise ratioehind a T-ring vortex shedder, with traversing hot wire probe.he signal to noise ratio for the inner ring was 10 dB higher thanhe outer ring. The repeatability of the pulses for inner ring wasix times higher than the outer rings. This shows that the detectionf inner ring vortices was the most appropriate choice in case of-ring vortex shedder. Popiel et al. [22] with the help of hot filmedge probe demonstrated the location of high signal amplitudes

s 1 mm behind the trailing edge of the cylinder with a slit. Turnert al. [21] studied several bluff bodies with spectrum analysis of hotire probe. Based on quantitative comparison of periodic wakes ofifferent bluff bodies, an improved vortex generator was evolved.he vortex generator was a cylinder with a slit and concave rearace shown in Table 4. Bentley et al. [49,50] and [25] studied var-ous dual bluff body combinations with two hot wire probes andbtained an optimum design condition. However, these have noirect significance related to vortex flowmeter design due to thebsence of blockage effects.

.3. Modern computers and vortex flowmeter

It is worth mentioning the impact of modern computers inhe evolution of vortex flowmeter design. Although, hot wirerobes and flow visualization techniques contributed significantly

n detecting the appropriate location of the sensor, qualitativeetailed flow field information was difficult to obtain using theseools. In the last two decades rapid development in high speedomputations motivated various researchers to address the flowhysics behind vortex shedders for flowmeter application.

In the early stages finite difference and discrete vortex methodsere used for numerical computations. Johnson [51] attempted

tream function-vorticity approach for two dimensional flowround circular cylinder and a commercial vortex shedder. The vor-ex shedder for the commercial flowmeter was a T-shaped shedder.he obtained Strouhal number was 1.31, which was within 10% ofhe empirical values. Matsunaga et al. [52] used commercial codeCRYU based on finite difference approximation. The results of twoimensional modelling of trapezoidal vortex shedder were com-ared with LDV (laser doopler velocimetry) measurements. Thetrouhal number obtained from numerical simulations was in closegreement with the experimental results. Wahed et al. [53] usedtream function-vorticity based approach to model flow around-shaped shapes of bluff bodies. Turbulence was modelled usingaldwin-Lomax model. The interesting outcome of this work was

dentification of secondary vortices near the meter wall and frontace of the vortex shedder. Lavante et al. [23] used commercial codeapable of solving the Navier-Stokes equation for three dimensionaleometries. Several vortex shedder shapes were investigated andased on numerical simulation an improved hydrodynamic shapeas suggested. The numerical results were compared with exper-

mental results obtained from ultrasound based measurements.Sun et al. [36] used commercial software FLUENT and vali-

ated duct wall differential pressure method with experimentalesults. Sun et al. [36] suggested optimum combination of tap loca-ions based on three dimensional numerical simulations with the

elp of commercial software FLUENT. The vortex shedder stud-

ed was a trapezoidal cylinder. Detailed investigations on the floweld pointed out that the amplitude of pressure pulsations wereaximum in a plane inclined at 45◦ to the bluff body axis. Jan

ctuators A 170 (2011) 8– 23

et al. [54] highlighted the effectiveness of dual bluff bodies forvortex flowmeter application. Numerical simulations were carriedout using operator splitting technique, balance tensor diffusivity,and an element by-element conjugate gradient iterative solver. Fuet al. [28] performed Large Eddy Simulations on dual triangulatebluff bodies using commercial software FLUENT. The numericalsimulations revealed that the axisymmetric points located on thedownstream of the second bluff body generate large pressure fluc-tuations for tracking vortex shedding frequency. Reik et al. [55]studied the performance of vortex flowmeter using commercialsoftware (STAR-CD). Turbulence was modelled with Reynolds aver-aging Navier-Stokes (RANS) equation. The comparison of numericalsimulation results with experiments results showed that RANSmodel was capable of predicting vortex shedding. The time stepselection is a very important aspect of the simulation process tocorrectly predict the vortex shedding frequency. Large time stepsmay hamper the accuracy of frequency measurement, too small atime step takes enormous time to march to the final solution. Thetime step size can be selected based on the flow rate and numberof sample points in one period. Younis et al. [56] suggested someguidelines in time step size selection based on the Reynolds numberand free stream velocity.

Flow field investigation played a pioneering role in the devel-opment of improved vortex shedders. Detailed flow physicsinformation highlighted various interesting observations, whichenhances the designers understanding related to vortex flowme-ters. The presence of wall makes the vortex shedding in pipe highlythree dimensional. This requires three dimensional simulations topredict the performance of the flowmeter with end wall effects.For practical engineering applications of vortex flowmeter simula-tions, realizable k-� and k-� RNG turbulence models can be used topredict vortex shedding with reasonable accuracy. However, highspeed computations needs to be carried out with direct numeri-cal simulations to predict real three dimensional vortex sheddingphenomenon.

5. Installation effects

Flow meters are always calibrated under fully developed con-ditions. Any distortion from fully developed conditions may causeabrupt changes in the calibration constant (linearity of Strouhalnumber) leading to false results. In industrial flow situation,flow distortion due to bends, control valves, pressure regulatingvalves, thermo-wells, de-superheaters, traps, gasket protrusions,misalignments, etc., are unavoidable. Manufacturers of vortexflowmeters therefore recommend some distance upstream anddownstream of the flow meter, so that they perform as per their lab-oratory calibration. The typical upstream and downstream lengthrequired for vortex flowmeters are 20D and 5D, respectively. Pro-viding such large upstream and downstream lengths may howeverbe difficult (especially when diameters are large). Therefore, a priorknowledge of the sensitivity to upstream disturbances for a specificvortex flowmeter is will be beneficial.

Flow distortions can be classified as asymmetry in velocity pro-files (caused by bends in plane) and swirl (caused by out of planebends, control vales etc.). Presence of small asymmetry in velocityprofile may change the calibration constant of the vortex flowme-ter. This error can however be corrected if the sensitivity of theflowmeter to such distortions is known. On the other hand highswirl flows can inhibit the vortex shedding altogether; the sig-nal quality therefore deteriorates considerably and hence cannot

be corrected. Mottaran [57] studied the performance of vortexflowmeter with rectangular bluff body under disturbed conditions.The disturbances introduced were single 90◦ bend and a pair of off-set (out of plane) 90◦ bends. The effect of surface roughness inside

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he pipe was also reported. The roughness was introduced with theelp of a sand paper (grade 3 0.5 linings). A 3% increase in Strouhalumber was observed in presence of roughness as compared to

hydraulically smooth pipe. Volynkin et al. [58] suggested a pro-edure to estimate the errors associated with surface roughnessffects. Systematic sets of experiments were carried out with var-ous surface roughness pipes and correlations were generated forhe calibration constant.

Takamoto et al. [59] studied the effects of pipe fittings on vortexowmeter. Experiments were carried out in a test line of 150 mmiameter with water as the working fluid. The Reynolds numberange covered was ReD = 2 × 105–106. Six types of piping config-rations (a single bend, double bend in the same plane, doubleend out of plane, an expander, a reducer and a gate wall) wereested at various upstream distances. The effect of upstream dis-ance was measured by changing the upstream length (betweenhe upstream fitting and the flowmeter) from 5 to 55D. Four kindsf commercially available vortex flowmeters were examined. Theowmeter was examined at two different angles � = 0◦ and 90◦ (�

s the angle between the axis of bluff body perpendicular to theage and the plane in which the pipe fitting lies) to take care ofon axisymmetric velocity profile. The installation effect was mea-ured as a deviation from the experimental installation condition inhich the upstream length was 100D. Swirling flow was observedith double bend manifested by negative deviation in calibration

onstant, which was an indication of decrease in the frequency ofortex shedding.

Laneville et al. [60] investigated the performance of vortexowmeter in the presence of swirling flows with the help of hotire anemometer. The bluff body used was trapezoidal in shape.

ts frontal dimension was 23 mm and base was 21.5 mm (block-ge ratio 0.293). The experiments were carried out for a Reynoldsumber ReD = 1.45 × 105. It was observed that the signal amplitudeeduces with increase in swirl index (ratio of difference betweenotal flow rate and axial flow rate by the total flow rate). Miaut al. [61] studied the performance of vortex flowmeter with twolbows out of plane at Reynolds number between ReD = 7.8 × 104

nd 2.1 × 105. Experiments were carried out in a 50 mm piping withater as the working medium. The vortex flowmeter used was a

onventional type in which the piezoelectric sensor was embeddedn the T-shaped vortex shedder. Mean flow field downstream of thelbows was observed with a cobra probe. The width (d = 10.7 mm)nd the length of the extended plate of the shedder was d = 10.7 mmnd 2d, respectively. The uncertainties of the vortex shedding fre-uencies measured at the inlet were within a range of ±0.12–0.17%nd the uncertainties of the vortex shedding frequencies measuredt 45D were in the range of ±0.32–0.58%. The quality of the sig-al obtained at 15 and 16D appeared to be the best among all the

ocations examined. The Strouhal number values in these locationsere within ±0.129–0.001%, where 0.129 is the reference value at

ully developed turbulent pipe flow regime. The axial flow distribu-ion obtained at 15D was much more uniform than those obtainedt other locations, which was attributed to the pronounced decayf the swirl intensity within 15D downstream length. The reasonor getting high quality signal at 15D was attributed to the unifor-

ity of the axial velocity distribution at this location, which wasesponsible for suppression of low frequency modulations in theortex shedding signal measured. Yang et al. [62] studied the effectf perforated plate upstream to the vortex flowmeter as a sourcef disturbance. A vortex flowmeter with piezo sensor downstreamf the bluff body and a commercial vortex flowmeter (YokogawaF105) were compared. The study revealed that piezo sensor down-

tream the bluff body was more sensitive to turbulence due topstream disturbance compared to the commercial flowmeter.

Fluid pulsation caused due to pumps, compressors, valves andtructural vibrations are one of the most challenging installation

ctuators A 170 (2011) 8– 23 15

effects, which need to be addressed very carefully. Wolochuk et al.[63] performed experimental investigations on the combined effectof turbulence and unsteady velocities on the performance of vortexflowmeter. The bluff bodies studied were triangular in shape. TheStrouhal number was found out to be dependent on turbulenceintegral length scale.

The increase in upstream turbulence intensities from 2.5 to 10%results in 2.4% increase in Strouhal number for turbulence integrallength scale of 0.5d. However, the turbulence length scale of 3dreduced the Strouhal number by 26% for turbulence intensities of10%. Lock-on phenomenon was observed for various frequencies(fp ≈ f, 2f, 4f) of periodic unsteady upstream velocities. However,no lock-on phenomenon was observed for fp < f up to 16% ampli-tudes. These results laid down some recommendation for practicalapplication of vortex flowmeter. The vortex flowmeter should becalibrated in turbulent flows with turbulence intensities and lengthscales of magnitude which practically exists in real application.Use of smaller size bluff bodies was recommended, to avoid lockon and to reduce turbulence intensities. Although the experimentsare conducted in square channel wind tunnel where in pipe cur-vature and end wall effects were absent. These results highlightedsome of the practical upstream effects on the performance of vortexflowmeter, which needs to be explored with real vortex flowme-ters. Hebrard et al. [64] reported the fluid pulsation amplitudeeffects on the performance of vortex flowmeter. Lock-on phe-nomenon was one of the devastating effect, which hampers theperformance of the meter altogether. This occurs when fp ≈ 2f. Asmiet al. [65] studied with the help of experimental investigation theeffect of bluff body shapes on the lower limit of reduced velocityUr which causes lock-on effects. The commercial bluff body shapes(triangular and T-shape) were found out to be more influenced byflow pulsations compared to unconventional (flat plate and rect-angular) shapes. Hu et al. [66] and [67] elaborated various regimesof vortex shedding based on frequency ratio (f/fp) as quasi-steady,hysteresis and non-interactive. However, the study was morefundamental rather than directly applicable to vortex flowmeterperformance.

Rossberg et al. [68] suggested a mathematical model to pre-dict inappropriate installation effects on the performance of thevortex flowmeter. The process of vortex generation was describedby Stuart–Landau equation and with the use of scaling factorsof Navier–Stokes equation, the installation effects (deviation inStrouhal number) with 0.5% were detected. Cambier et al. [69] stud-ied the effect of radius of single 90◦ bend, in-plane double bend anda three-dimensional 90◦ out-of-plane double bend. The deviationfrom standard condition in case of double bends was 1.88% and2.45% numerically and experimentally, respectively.

Venugopal et al. [37] studied the installation effects on the per-formance of vortex flowmeter with duct wall differential pressuremethod. The effect of blockage under disturbed conditions was alsoreported for trapezoidal bluff body. Swirling flow caused amplifica-tion of signal amplitudes as compared to fully developed conditionsfor 0.24 blockage ratio. Blockage ratio of 0.3 was reported to be thebest among all other blockages studied. The minimum upstreamlength with gate valve 50% open was 11D with Laws vanes flow con-ditioner. The impact of upstream disturbance on vortex sheddingat various upstream distances is shown in Fig. 6. Not only upstreamlength but the downstream length also affects the performance ofthe flowmeter. These effects are seldom reported in the literature.Pipe vibration is another source of disturbance which affects theperformance of the vertex flowmeters, especially with mechanicalsensors such as piezoelectric and capacitive. Peter et al. [70] studied

the impact of pipe vibration in vertical direction of magnitude 1 gon the performance of vortex flowmeter. The most severe effects ofpipe vibrations were at no flow situation. Under no flow situations,the sensor picks up the vibration signal and displays some mislead-

16 A. Venugopal et al. / Sensors and Actuators A 170 (2011) 8– 23

Fig. 6. Vortex shedding under disturbed conditions (Venugopal et al. [37]).

A. Venugopal et al. / Sensors and Actuators A 170 (2011) 8– 23 17

Table 1Upstream length requirement suggested by various authors.

Author Bluff body D1 D2 D3 D4 D5 D6 D7 F

Motharan [57] Triangular 45D 45D – – – – 30D 10DTakamoto et al. [59] Trapezoidal T-Shaped 13D 12D 43D 14D 16D 5D 16D –Miau et al. [61] T-shaped 15D – – – – – –Venugopal et al. [37] Trapezoidal – – – – – – – 11DEMCO [75] – 10D 15D 30D – – – 30D –KROHNE [2] 20D 30D 40D 20D – – 50D –

Orifice 23D 25D 40 D 15D 27D 15D – –

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ng reading. The effect of vibration is severe at low flow rates wherehe amplitude of vortex signal is small.

The literature suggests that the vortex flowmeters are sen-itive to upstream disturbance, especially to swirling flows. Theinimum upstream length requirements for various disturbances

uggested in the literature are tabulated in Table 1. A comparisonith orifice plate of diameter ratio 0.8 is also made. The table shows

hat the installation effects are highly dependent on the shape ofhe bluff body. Unfortunately, there are no general guidelines fornstallation effects; each vortex shedder and sensor combinationseeds to be studied individually under disturbed conditions. Mostf the vortex flowmeter manufacturers recommend upstream andownstream length requirements in product installation manual.ome of the vortex flowmeter manufacturers have incorporatedome correction factors to accommodate installation effects. Fluidulsation effects are studied to some extent on the performancef vortex flowmeter however; the real tackling strategies for suchssues are seldom reported.

. Signal processing

The signal processing associated with vortex flowmeters areery challenging. The vortex shedding frequency obtained fromny type of sensor will always be embedded with hydrodynamicoise, mechanical vibrations and electrical interference. The most

mportant characteristic of signal processing is high sensitivity atow flow rates. The method should be able to count vortex pulsesccurately at low flow rates, where the vortex strength is week.very meter size and fluid has a respective range of vortex fre-uency. Frequencies above and below this range are not requiredor a specific size. To increase the signal to noise ratio (SNR) theserequencies are usually cut off with the help of band pass filters.limination of any undesired noise close to the vortex sheddingrequency is always a challenging task. Hydrodynamic noise arehe most difficult to eliminate as they are generated along with theortex. The fast Fourier transform, wavelet transform, notch filternd digital filtering algorithms are widely used to compute vortexhedding frequency. Amadi et al. [71] analysed the vortex flowme-er signal of commercial vortex flowmeter manufacturer (Foxboro).he zero crossing and spectrum analysis techniques were used tostimate the vortex shedding frequency. The perturbations in theow modulate the formation of the vortex and were manifesteds the randomness in the vortex flowmeter signal. This makes therocessing of vortex signal complex.

Chen et al. [72] proposed a signal processing based on flowomentum method to estimate the vortex frequency at low flow

ates. The amplitude of the signal was assumed to be proportionalo (� × V2), which implies ((m/A) × V). The vortex signal was fil-ered with the help of a group of second order low pass filters. The

ltered signal was fed to the comparator and the pulse countero estimate the vortex shedding frequency. The turndown ratioovered in present study was 1:25. However, the lower rangef Reynolds number (28,000) was still on the higher side. Zheng

◦ bends out of plane; D4, reducer (2D to D); D5, expander (D to 2D); D6, gate valve

et al. [73] proposed double window relaxing notch periodogrammethod to estimate the vortex frequency, when the frequency bandof noise and vortex frequency are in same range. Frequency andamplitude were estimated using Hanning and triangular windowsrespectively. The uncertainties associated with this method werebelow 1%. Sun et al. [74] proposed a method based on empiri-cal mode decomposition to diagnose the vortex flow meter signalunder various flow conditions. The proposed method was capa-ble of extracting all the oscillatory modes embedded in the vortexflowmeter signal. The effects of pipe vibration and air bubbles inthe flow on the quality of the signal were also demonstrated.

Akresh et al. [76] proposed smoothing of vortex flow signalbased on Kalman filters. Zero crossing technique was used toestimate vortex shedding frequency. Band pass filter was usedto remove undesirable frequencies. The filtered signal was fur-ther smoothened with the help of Kalman filter. This method hadincreased the operating range of the flowmeter by 55% on the upperrange of Reynolds number.

Hu et al. [77] proposed a digital signal processing method basedon auto-correlation and fast Fourier transform. The amplitude ofthe vortex signal was correlated with the frequency of vortexshedding. The raw signal of the vortex flowmeter was fed to thiscorrelation to estimate a central frequency. A digital band passfilter was designed based on this central frequency with cut-offfrequencies as 0.7 and 1.3 times the central frequency. Autocorre-lation of the filtered signal was used at low flow rates to estimatethe exact vortex frequency. At high flow rates fast Fourier trans-form was used. At low flow rates, the uncertainties are higher withfast Fourier transform due to poor frequency resolution. Hence, acombination of autocorrelation and fast Fourier transform tech-niques reduced the overall error in vortex frequency estimationbelow 0.3%. Xu et al. [78] proposed a new method to estimatethe vortex shedding frequency under mechanical vibration noise.Autocorrelation method was proposed to capture the signatureof the vortex signal and the noise. The periodic jitter associatewith vortex signal characterises the vortex signal as a broad bandsignal. However, the mechanical vibration noise always occurs atfixed frequency. The distinguishable features of vortex signal andnoise were observed in the autocorrelation function. The ampli-tude of autocorrelation function of the vortex signal will attenuatequickly with time, whereas that of noise attenuates slowly. Thismethod was implemented in super low power micro controller intwo-wire mode of meter operation. The algorithm was tested suc-cessfully under mechanical vibration noise on water rig. Ukil et al.[79] proposed a digital signal processing based diagnosis of vortexflowmeter signal under no flow conditions. A piezoelectric sensorcaptures pipe vibrations caused by pumps and valves under no flowconditions and the meter misleads by showing some flow rate. Theproposed method was based on frequency computation and detec-

tion of reciprocal or integral harmonic under no flow conditions.This was accomplished by performing harmonic analysis of fre-quency profile. Zhang et al. [80] and Laurantzon et al. [81] proposedwavelet based method to estimate the vortex shedding frequency.

18 A. Venugopal et al. / Sensors and Actuators A 170 (2011) 8– 23

Table 2Signal quality parameters.

In – Energy associate with noise

In =

R∫i=0

Aidf Turneret al.[21]

An = InR

SNR = AcAn

Regularity = f

b, sensitivity = Cp′ , Cp′ = (p′)0.5

0.5�U2m

f – vortex shedding frequency; Um – average flow velocity; p′ – fluctuating component ofpressure

Igarashi [24]Peng [26]and [27]

Mmod(SNR) = p0n∑

i=1

Piωi

ω =

⎧⎨⎩

exp

[−2.83

(fif

− 1

)]

exp

[−2.83

(f

fi− 1

)]⎫⎬⎭

fi ≤ f

fi > f

p0 – power of vortex shedding frequency; Pi – power of other frequency component; fi – meanfrequency; f – vortex frequency

Pankanin et al. [82]

SNR(dB) = 10log10P0

PrP0 =

1.02f∫0.98f

P(w)dw

Pt =

we∫0

P(w)dw Pr = Pt − P0

ctrum

Miau et al. [20]

ftmsthtpvett

tipOoqsesw

P(w) – energy content in frequency component (w); Pt = total energy of the speupper bound frequency in the spectrum – sampling rate

In the recent past, few commercial vortex flowmeters manu-acturers have also introduced digital signal processing algorithmso efficiently filter out undesirable signals. Implementation of these

ethods with low power 2-wire system was a big challenge in earlytages of vortex flowmeter development. But most of the manufac-urers have achieved this in the recent past. Few manufacturersave even come up with multi variable type flowmeters to gethe mass flow rate directly with pressure and temperature com-ensation (density measurement). This has increased the use ofortex flowmeters for steam and compressed gas metering consid-rably. The non-linearity at low Reynolds number is tackled withhe piece-wise linearization techniques suitably implemented inhe electronics.

Some of the definitions of signal to noise ratio and other parame-ers related to vortex signal reported in the literature are tabulatedn Table 2. This will help the designer to judiciously evaluate theerformance of the meter output in terms of these parameters.ne of the advantages of vortex flowmeter is that the amplitudef the signal is not important for flow rate calculation, only fre-uency measurement is sufficient. However, the sensitivity of the

ensor and electronics should be high enough at low flow rates tostimate vortex frequency at reasonable accuracy. At low flow ratesometimes the vortex signal and noise are of comparable strength,hich needs to be handled carefully.

; we –

Comparison of signal qualities based on the signal to noise ratiodefinitions provided by Miau et al. [20] and Turner et al. [21]. Thesignal was obtained by duct wall differential pressure method fora trapezoidal bluff body of blockage ratio 0.3 [37]. The SNR valuesfor two different velocities 1.35 and 3.95 m/s are shown in Table 3.Discrete Fourier transform was performed to compute the vortexshedding frequency for four sets of data points at a given veloc-ity. The SNR values obtained by using Turner et al. [21] definitionalways yield positive numbers as this is the ration of amplitude ofvortex peak and mean noise peak. The signal quality judgement wasdifficult with this definition. However, the SNR values obtained byusing Miau et al. [20] definition reveal interesting insights into vor-tex shedding phenomenon. The SNR values are not always positivefor a given velocity. The randomness in the SNR values manifestthat the shedding process is not truly periodic. Another interest-ing observation is the SNR values are not proportional to the flowvelocity. This suggests that the hydrodynamic noise also magnifiesas the velocity increase giving almost same SNR values at lower andhigher operating flow rates. The power spectrum for two differentvelocities 1.35 and 3.95 m/s are shown is shown in Fig. 7. The broad

width of the peak and other secondary peaks makes the SNR valuesnegative.

This shows that periodic jitter in the vortex frequency andhydrodynamic noise mainly defines the quality of the signal from

A. Venugopal et al. / Sensors and Actuators A 170 (2011) 8– 23 19

Table 3SNR values at different velocities.

Velocity (m/s) ReD Frequency (Hz) St SNR

Miau et al. [20] Turner et al. [21]

1.35 146000 13.33 0.27 1.3 53213.32 0.27 3.15 140012.71 0.26 0.09 40013.33 0.27 −0.26 488

3.95 398000 34.97 0.26 1.13 42434.71 0.27 −1.19 39235 0.26 −2.92 28836 0.27 1.5 590

16012080400Frequency (Hz)

0

200

400

600

800

1000

Pow

erde

nsit

y(W

/Hz)

V = 1.45 m/sf = 13.3 2 HzSNR = 3.2

16012080400Frequency (Hz)

0

200

400

600

800

Pow

erde

nsit

y(W

/Hz)

V = 1. 45 m/sf = 13.33 HzSNR = - 0.26

160120804000

4000

8000

12000

Pow

erde

nsit

y(W

/Hz)

V = 3.95 m/sf = 36 HzSNR = 1.5

160120804000

2000

4000

6000

8000

10000P

ower

dens

ity

(W/H

z)

V = 3.95 m/sf = 34.37 HzSNR = - 2.9 2

um at

trrttio[

ueflfbd

7

Fbpocfo

vortex shedder reflected two separation points on the piezo sensor.This irregular behaviour in the flow separation generated irregu-lar fluctuations in the lift coefficient. The power spectrum was notvery clean. However, at higher velocities the peaks were clearly

K

Kmin

Kmax

Linearity

Kmean

±%

Designated Linear Range

Uncertaint y Ba nd

Frequency (Hz)

Fig. 7. Power spectr

he sensor. Comparable secondary peaks are observed at high flowates very close to the main peak. This increases the ambiguitieselated to vortex frequency choice. Considering highest peak ashe vortex frequency sometimes may be misleading, hence effec-ive filtering near the vortex frequency are essential. However, its advisable to remove the individual peaks one after other and tobserve the decay of autocorrelation function suggested by Xu et al.78] to identify the undesirable noise.

The signal processing associated with vortex flowmeter hasndergone drastic improvements, due to advancements in micro-lectronics and digital signal processing techniques. Elimination ofuid pulsation and pipe vibrations in the range of vortex shedding

requency (lock-in phenomenon) are the most important contri-utions in the development of vortex flowmeters contributed fromigital signal processing techniques.

. Measurement uncertainty

Measurements are always subjected to inevitable uncertainties.or vortex flowmeter the universal non dimensional Strouhal num-er is usually represented in terms of K-factor (number of vortexulse accumulated for a given flow in a given time). The calibration

f vortex flowmeter is insensitive to properties of the fluid like vis-osity, density, pressure and temperature and can be maintainedor long period. This is primarily because the K-factor is determinednly by the shape and size of the vortex shedder. The linearity of the

Frequency (Hz)

different velocities.

flowmeter is essentially the linearity of the K-factor with Reynoldsnumber. The typical K-factor plot with Reynolds number is shownin Fig. 8 along with uncertainty band and linearity.

The effect of manufacturing tolerance plays an important rolein obtaining the standard K-factor. Lavante et al. [83] with thehelp of numerical simulations provided some insight in to the flowphysics associated with manufacturing tolerances. A 1 mm shift inthe location of the piezo sensor in the vertical direction behind the

ReD

Fig. 8. Linearity of K-factor with Reynolds number.

20 A. Venugopal et al. / Sensors and Actuators A 170 (2011) 8– 23

Table 4Dimensions of optimum bluff bodies.

Author Shape Dimensions KL and St ReD

Igarashi [24]

s

d s/d = 0.1, d/D = 0.2–0.267 KL = 0.48–0.74,St = 0.26

ReD = 1.9 × 104 to2.5 × 105

Poipel et al. [22]

s

d s/d = 0.16, d/D = 0.16 KL = 0.57, St = 0.2 ReD = 250–43,000

Sun et al. [36]

d

L

d = 14 mm, L = 17.5 mm KL = 2.2, St = 0.25 ReD = 9.42 × 103 to8.48 × 104

Venugopal et al. [37] � = 72◦ , d/D = 0.28–0.3 KL = 2.2, St = 0.27 ReD = 2 × 105 to4.1 × 105

Zhang et al. [35] d d = 14 mm, � = 60◦ , d/D = 0.28 KL = 1.7, St = 0.26 ReD = 5.59 × 103 to1.67 × 105

Miau et al. [20]

a

d b

L

d = 32 mm, a = 3 mm, b = 10 mm, � = 45◦ , L/d = 1.56–2, d/D = 21.3 KL = 0.42, St = 0.15 ReD = 2 × 103 to1.8 × 104

Peng et al. [26]d d

d = 13 mm, d/D = 0.26, L/d = 4.6–5 KL = 2.6, St = 0.25 ReD = 5.59 × 103 to1.67 × 105

N

otwuualfKpt

fawuacwtrw

L

ote: The pressure loss coefficients (KL) are evaluated at ReD = 1 × 105.

bserved. The effect of rotation of the bluff body by 2◦ about theransverse axis, showed amplitude modulations but the frequencyas clearly identified. Ricken et al. [84] studied the effect of man-facturing tolerance on the performance of vortex flowmeter withltrasonic sensors. The bluff bodies used were triangular and rect-ngular in shape. The nonlinearities in the meter factor were high atarge angle of incidence due to abrupt increases in vortex sheddingrequencies. Ohki et al. [85] suggested that the nonlinearities in the-factor can be improved with the use of end plates between theipe wall and bluff body. End plates of 5 mm thickness improvedhe accuracy range for ±1% up to ReD = 1.0 × 104.

Baker [86] reported random production uncertainty in the K-actor of order ±0.8% for 50 mm meters, ±0.4% for 75 mm metersnd ±0.3% for 100 mm meters. An error of 0.1% in the blockage ratioill shift the K-factor by 0.13%. Miau et al. [87] reported the totalncertainty in the Strouhal value as deduced from a Fourier spectralnalysis to be ±0.745%, and the linearity as ±1.78%. However, pulseounting method gave the total uncertainty in K-factor as ±0.568%,

ith the linearity of ±1.89%. The bluff body was a T-shaped and

he experiments were conducted in air for a Reynolds numberange ReD = 2.56 × 104–1.56 × 105. The major source of uncertaintyas the frequency resolution at low flow rates. At low flow rates

auto-correlation was advised and at high low rates Fourier spec-tral analysis was found out to give superior results. Sun et al.[36] reported uncertainty evolution for a trapezoidal bluff bodywith duct wall differential pressure method in the Reynolds num-ber range ReD = 9.42 × 103–8.48 × 104. The uncertainties associatedwith calibration system were small compared to the vortex fre-quency measurement. The maximum uncertainty was 5.4%. Themajor contributing factor in uncertainty was the frequency resolu-tion. Venugopal et al. [37] reported uncertainties with wall pressuremeasurement method as 3.5%.

The contribution of Takamoto et al. [88] was one of themost important efforts in the last decade to standardise vor-tex flowmeters. Systematic set of experiments were carried outwith various bluff bodies in an attempt to optimize the same.The experiments were carried out in Reynolds number range theReD = 1 × 105–2 × 106. The K-factor sensitivity for each flowme-ter was studied under both fully developed and disturbed flowconditions. Dry calibration uncertainties associated with these

flowmeters were 0.12%. For trapezoidal vortex shedder blockageof 0.28 was reported as the optimum.

ASME–FMC-6M-1998 [89] elaborates some guide lines in uncer-tainty evaluation related to estimation of the vortex shedding

and A

fitbe

eiwwd

8

opmttpmnfsdetimtSdm

tbeRabdtrsr

9

bvpvwesodto

vtr

A. Venugopal et al. / Sensors

requency. The hydrodynamic noise causes periodic jitter (changen time period) for vortex shedding cycles. This inevitably gives riseo mean and standard deviation in the shedding period. The cali-ration time required for a given geometry and flow rate can bestimated for desired uncertainties from these guidelines.

A compilation of all optimum vortex shedders reported in the lit-rature has been undertaken by the present authors and presentedn Table 4. The pressure loss coefficient for these vortex shedders

as also obtained numerically with the help of commercial soft-are FLUENT. The information in the table is expected to help aesigner to choosing an appropriate vortex shedder shape.

. Vortex flowmeters and two phase flow

The major share of vortex flowmeter market is for measurementf steam flow. This includes process industries, building heating,ower plants etc. Unfortunately the performance of vortex floweters is seldom reported for steam application in the open litera-

ure. However, some work is reported in the literature for air-waterwo phase flow. Sun et al. [90] conducted experiments in horizontalipe flow with trapezoidal bluff body and air-water two phase flowixture. The linearity of vortex shedding frequency with Reynolds

umber was observed till void fraction of 18%. Beyond 18% voidraction, the signal was highly distorted and it was difficult to mea-ure the vortex shedding frequency. The signal amplitudes wereeteriorated with increased void fraction. Sun et al. [91] performedxperiments in vertical pipe flow with air-water two phase mix-ures and suggested correction factor based on the ratio of K-factorn single phase and two phase flow to improve the accuracy of the

eter. At higher void fraction the vapour molecules gets trapped inhe low pressure wake region, which results in poor signal strength.un et al. [92] studied the performance of vortex flowmeter withuct wall differential pressure method under two phase air-waterixture condition.The stability of vortex shedding was found out to be a func-

ion of void fraction, which reduces with void fraction. Theubble vortex shedding frequency was found out to be a lin-ar function of two phase flow Reynolds number in the rangeeD = 9.47 × 104–20.44 × 104. The literature shows few preliminaryttempts to understand the complex two phase flow as applica-le to vortex shedding. This needs to be investigated in greaterepth to address, particularly steam water two phase flow effect onhe performance of vortex flowmeter. Most of the manufacturersecommend vortex flowmeters for superheated and dry saturatedteam application. The limiting value of thermodynamic qualityecommend by most manufacturers is 0.95.

. Conclusions

The artistic painting of great painter Leonardo da Vinci hasecome a commercial asset in the modern world in the form of theortex flowmeter. The investigation revealed by the researchersertinent to flow around circular cylinder has become the basis forortex flowmeters design. The design of vortex flowmeter beginsith the selection of appropriate vortex shedder shape. The sharp

dge vortex shedders are the first choice for this application. Theharp edge bluff bodies ensured fixed separation point irrespectivef Reynolds number range. Improved vortex shedders like cylin-er with a slit and cylinder with a slit and concave rear face arehe most promising ones from stability and repeatability pointf view.

Cylinder with a slit was the first break-through design for theortex flowmeter. Later, few researchers modified and improvedhe performance of the cylinder with a slit by introducing concaveear face. T-shaped vortex shedder is having promising features by

ctuators A 170 (2011) 8– 23 21

stabilizing the low frequency modulation associated with the vor-tex shedding. Axi-symmetric ring type vortex shedders possessessome advantages like low permanent pressure loss. The detectionof vortex signal is difficult with passive devices. Active devices likeultrasonic sensor need to be explored with axi-symmetric ring typevortex shedders. However, it is worth mentioning that, most ofthe commercial vortex flowmeter manufacturers are using simpleshapes like trapezoid and triangle. The main reason behind thischoice may be the ease in manufacturing simple shapes and patentinfringements associated with improved vortex shedders. Hence,there is a need to explore new vortex shedder shapes.

The blockage ratio should be in the range of 0.2–0.3 to obtaingood results. The clamping of vortex shedder body inside smallerdiameter pipes needs to be addressed carefully. Small protrusionsinside the pipe close to the vortex shedder may cause severe non-linearity in Strouhal number.

The biggest challenge in developing vortex flowmeter is theselection of the sensor. Most of the sensing technologies reportedin the literature are very challenging to realize as a product. Thesesensors are not readily available in the market. The design aspectsrelated to the sensors are not reported in the literature. This againmay be attributed to patent laws. However, differential pressureand piezo-sensors seem to be the first choice on the basis of easein implementation. The sensor and the vortex shedder must beoptimized both from vortex shedding mechanism and signal pro-cessing aspects. The location of the sensor relative to the bluff bodyis very important to achieve high sensitivities at low flow rates.The details of location of the sensor are seldom reported for piezo,ultrasonic and capacitive sensors. Some guide lines are availablefor the location of differential pressure sensors in the literature.The non dimensional tap location for differential pressure sensorreported for various blockages is 0.714 times the diameter of thepipe times the blockage. The cost and signal processing associatedwith ultrasonic sensors are very expensive and complex.

Flow field investigations using commercial computational fluiddynamics software have become the first choice of the designer forvortex flowmeter design. Optimization of bluff body shapes andrelative location of the sensors can be simulated with reasonableaccuracy using realizable k-ε and k-ε RNG turbulence models. Thefinal design can be validated with experimental investigations.

The sensitivity of vortex flowmeter to installation effects needsto be studied individually for each vortex shedder and sensor com-bination. There are no general guide lines available in the literature,which can be directly used. The application of vortex flowmeters fortwo phase flows like steam are not addressed to a great extent in theliterature. Some preliminary studies are available with air–watertwo phase flow mixtures, which can be used as a guide lines. Appli-cation of vortex flowmeter with wet steam (thermodynamic qualitybelow 0.95) is not recommended. The uncertainties associated withsensing mechanism, signal processing and calibration methodologyneeds to be evaluated precisely. Some guide lines are available inASME–FMC-6M-1998, which can be used to estimate calibrationtime requirement for a desired accuracy.

The signal processing associated with vortex flowmeters hadcame a long way from analogue methods to modern digital sig-nal processing tools. Most of the literature reported suggests usingpower spectrum analysis to compute vortex shedding frequency.This method fails when noise due to mechanical vibrations arepresent in the system. Autocorrelations function is one of themost important method by which vortex frequency can be distin-guished by tracking the signature of vortex shedding frequency andmechanical vibration noise. The periodic jitter present in the vor-

tex frequency makes it a broad band signal, which can be seen inautocorrelation function. In the recent past vortex frequency esti-mation using digital signal processing tools are implemented andrealized in two-wire mode by some researchers.

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Process parameters like operating temperature, pressure,nvironmental and hazardous protection norms must also be incor-orated while designing the flowmeter. Since, vortex flowmeter is

universal design which does not change from application to appli-ation, the spare part inventory is very simple. The installation andperating cost associated with vortex flowmeter are also very lowompared to Coriolis, ultrasonic and turbine flow meters. In short,e can say that vortex flowmeter is one time investment.

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Biographies

Venugoapl A. was born in 1985. He received his B. Tech from NIT Raipur India (2006)and M. Tech from IIT Bombay India (2008). He worked for Forbes Marshall Pvt. Ltd.for two years on research projects related to flowmeters. At present he is pursuingPhD studies from IIT Bombay. His research area includes bluff body wake dynamics,flow metering and heat transfer.

Amit Agrawal obtained his B.Tech from IIT Kanpur in 1996. He worked at TataMotors, Pune for two years, before joining graduate studies at the University ofDelaware, USA. After obtaining his PhD in 2002, he spent about 2 years as postdoc-toral fellow at the University of Newcastle, Australia. He is currently an AssociateProfessor at IIT Bombay. His areas of interest are experimental, numerical and the-oretical investigation of turbulent flows and flow at the microscales.

S.V. Prabhu is currently an associate professor at the Department of MechanicalEngineering, Indian Institute of Technology, Bombay, India. He graduated with a B.E.(Mech. Engg.) first class with distinction from Mysore University in 1988, a Master of

Technology from National Institute of Technology, Surathkal in 1991 and a PhD fromIndian Institute of Technology, Bombay in 1998. His research interests are flowme-tering, heat transfer studies involving jet impingement, fire dynamics, renewableenergy (hydrokinetic turbines and wind turbines), gas turbine blade cooling andmelting and solidification of PCM and metals.