Indian Journal of Engineering & Materials Sciences Vol. 6, June 1999, pp. 119-124

Performance characteristics of an eccentric venturi meter with elongated throat for flow rate measurement of solid-liquid flows

S Bharania, R Mishrab

, S N SinghC & V Seshadric

"Department of Mechanical Engineering, Shri G S Institute of Technology and Science, Indore 452 003, India

"Department of Applied Mechanics, M.N.Regional Engineering College, Allahabad 211004, India

'Department of Applied Mechanics, Indian Institute of Technology, New Delhi 110 016, India

Received 22 July 1998; accepted 17 March 1999

The performance characteristics of an eccentric venturi meter with elongated throat for 68 mm NB pipeline having an area ratio of 0.327 for the measurement of flow rates in solid-liquid flow, have been investigated. The modi fied geometry of the venturi meter is expected to suppress the erosion rate caused by the motion of solid particles. Copper tailings obtained from a processing plant have been used with water to prepare the solid-liquid mixture. Experiments performed over a wide range of flow velocities and solid concentrations show that the value of discharge coefficient of the eccentric venturi meter with elongated throat is slightly higher for slurry flow as compared to the value obtained for clear water flow. It is also seen that the average value of discharge coefficient obtained at different solid concentrations increases marginally with increase in solid concentration. The redistribution of solids at the throat of the venturi meter has also been investigated at different solid concentrations.

Yenturimeter is a simple and reliable obstruction type of flowmeter. The characteristits of this meter, when designed as per the relevant standards are well understood and documented for the single phase f1ow l

. Over the years these meters have also been used for metering two-phase flows (gas-solid, solid­liquid). The performance of these meters in terms of value of discharge coefficient and pressure loss have also been investigated by several researchers2

-s for

two phase flows . Sharma2 and Lee J have investigated the flow of gas-solid mixture using conventional venturi meter, whereas Payne and Crowe4 have used a non-standard venturi meter for monitoring mass flow rate of similar suspensions . Graf5 has also proposed a modified venturi meter for measurement of flow rate of two phase flows. Brook6 and Hasan et aC have investigated the performance of conventional venturi meters for a particular type of slurry. Abbas and Crowe

x have analytically predicted the

characteristics of a conventional venturi meter for two phase flows by solving the fluid flow governing equations. Hirata et at.') have also proposed a method for predicting both the discharge and the in-situ concentration for a conventional venturi meter.

Although conventional venturi meter can be used for two phase flows , there are a few practical limitations as under.

(i) Horizontal pipelines transporting solid-liquid mixtures are subject to excessive wear specially at the bottom of the pipeline. Conventional venturi meter installed in the horizontal pipeline is also subjected to excessive wear because of increased velocity of solid particles in the converging portion . The nonuniform distribution of solid particles causes coarser particles to travel near the bottom of the pipeline and results in uneven wear of the meter surface. This implies that the discharge coefficient of a conventional venturi meter will keep changing with time due to excessive wear and hence renders the conventional venturi meters unsuitable for long term application .

(ii) It is also known that at low flow velocities , coarser particles do settle down at bottom of pipe thereby resulting in an unpredictable performance of the venturi meter.

In the present study, the cross sectional shape at the throat of a conventional venturi meter has been elongated towards the bottom of the horizontal pipe to overcome the abo ve mentioned practical

120 INDIAN J. ENG. MATER. SCI. , JUNE 1999

difficulties (see Fig.I). The discharge coefficient of the modifi ed venturi meter has been evaluated as a function of so lid concentration . Further, the solid distribution at the throat cross section of the venturiille te r as we ll as in the straight pipeline has also bee n measured to quantify the e ffect of the eccentri c geometry of the throat on the overall flow field .

Eccentric Venturimeter A conve nti ona l venturi meter of 68 mm NO having

a d iamete r rati o (diD) of 0.54 was modified at the throat to get an e longated e lliptical shape shown in Fig. I. The geometri c de tails o f thi s venturi meter are giv~n be low:

HID = 40/68 ang le o f conve rgence= 70 (Half Angle) ang le o f divergence= 30 (Half Angle) a rea of venturimeter th roat= 1/ 88 .0 mm2

area at the inle t and at the outlet of the venturimeter= 363 1.68 mm2 (di ameter = 68 mm) The throat o f the conventi onal venturi meter was

machined towa rds the bottom so that the bottom of the pipe became stra ight without any constriction (see Fig. I). The resulting a rea ratio was 0.327 and equi val ent di ameter ra ti o (d/D) of the modified

ven tur i meter is "" 0.572. The modified shape is ex pec ted to reduce the e rosi ve wear at the throat compared to conventi onal ventlirimeter as the constri cti on at the bottom of the modified ven turi mete r IS negli gibl e whe re particle co ncentrati on re mains hi gher as compared to the top port ion. Further. settling tendency of particles is expected to be less at the bottom of th is venturi meter design because o f minimal obstruction. With the red uc ti on in the obs tructi on, the pressure loss is a lso

CONNECTE D 10 MANOMET £R

\

0 : 68 mm

AIR HE t e ASE VALVE

./

H'=4 0 m m

11~ . lmj. 16 mm _I SECTION"dL E LEVA TlON

Ar A- A

Fig. I- Schemati c diag ram or the eccentri c ven turi meter wi th e longated th roa t

ex pec ted to be somewhat lower as compared to a conventional des ign.

The diffe renti a l pressure across the venturi meter is measured uSing pressure taps provided with separation chambers using U-tube mercury manometers ( least count of 0.5 mm) . The separation c hambers fi li ed with water are provided to act as inte rface between slurry and manometric fluid to prevent so l id particles from choking the connecting tubes (see Fig. I).

Experimental Set-up The pilot plant test loop used for the present study

is schemati ca ll y strown in Fig. 2(a). It consists of a

c losed circuit pipe test loop of 55 mm diameter having length of 60 m . For the purpose of present experimentation a straight length of 25 m was replaced by pipe of 68 mm diameter ( i.d.), as shown in Fig. 2a. The slurry was prepared in a hopper shaped mixing tank provided with a suitable stirring arrangement in order to keep the slurry well mixed . The slurry was pumped from this tank into the pipe loop by means of a slurry pump. The s lurry pump empl oyed was of suffici ent capacity to cover the entire range of head and discharge needed at a ll concentrations. The flow rate of the slurry in the pipe loop was varied over a wide range by suitab ly operating the plug-valve provided in the loop, near

Col

I"'TO SAMPLER

J~.-,,,,,, n " I.i~

6 f bJ (A ll d l rn~ns io "s in mm J

Fig. 2--{ a) Sc hc mati c layout or slu rry test loop facility, (b) Sampling tu he

BHARANI et af.: PERFORMANCE CHARACTERISTICS OF AN ECCENTRIC VENTURIMETER 121

the delivery end of the pump. Additional auxiliary control over the flow was possible through the operation of a by-pass line provided with the pipe loop. The two corresponding valves were adjusted so as to keep the head developed by the pump at an approximately constant value at all the velocities. After circulation through the pipe loop, the slurry was returned either directly to the mixing tank or diverted by means of a flow diverter to a measuring tank provided adjacent to the mixing tank. The flow rate could be ascertained by measuring the rise in the level of slurry in the measuring tank over a known time. A stirrer provided in the measuring tank kept the slurry in suspension during its use. The modified venturi meter as described earlier was fitt~d in the pipe loop as shown in the Fig. 2a.

A transparent observation chamber was provided in the pipe loop to facilitate visual observation of the flow. Thus, it was possible to observe the movement of the solid particles near the bottom of the pipe and to visually estimate the deposition velocity without disturbing the flow . The pressure taps with separation chambers were provided to measure the pressure drop in the pipe loop using U-tube mercury manometer.

The specific gravity of the slurry flowing through the pipeline system was monitored by collecting efflux samples through a efflux sampler provided in the vertical section of the pipe loop, near the discharge end . The average solid concentration was then evaluated from the measured specific gravity

using a predetermined correlation between the mixture specific gravity and the solid concentration. The measurement of the mixture specific gravity thus provided a rapid procedure for monitoring the solid concentration.

The solid di stribution inside the pipe and at the venturi meter throat is measured by traversing a concentration sampler (Fig. 2b). This concentration sampler collects the sample under near isokinetic conditions and has been shown to measure the in-situ local concentration quite accurately 10. Samples were collected at five different heights from the bottom of pipe at two cross sections: the first one in a straight pipe (YID= 0.09, 0.20, 0.45, 0.58 and 0 .91) and second one at the venturi meter throat (YID= 0.09, 0.20, O.4j, 0.58 and 0.7).The specific gravity of the s lurry co ll ected through the sampling tube at any section inside the pipe is measured and from this data variation of solid concentration along the mid vertical plane of the pipe/venturimeter throat is determined .

Properties of Solid Material Used

Solid material obtained from Copper processing plant has been used in the present investigation . The properties of solid material used are given in Table l.The static settled concentration of the slurry was determined ex perimentally by allowing the solid liquid suspension to settle in 1000 mL graduated jar. The rheo logical parameters characterising the

Table I--Physical properties of the copper tailings

(a)

(b) Overall specilic gravity of solids : 2.82 Particle size distribution:

Particle size, IJ % liner

R50

100

600

99.6

210 150 106

97.36 80.64 71.24

(c) Stati c se ttll~d concentration : 58.67 % by weight (d) Rheological data:

cw ,% Tcmp., oC Yield stress, dynes/cm2

0 19 0

10 19 0

20 19 0

30 19 0

40 19 0

75

52.01

Viscosity of slurry, cP

1.141

1.271

1.509

1.982

53 48 21 16 8 6

40.50 37.62 26.78 16.61 4.07 3.73

Viscosity of Relative Remarks water, cP viscosity

1.03 1.0 Newtonian

1.03 1.108 Newtonian

1.03 1.234 Newtonian

1.03 1.465 Newtonian

1.03 1.924 Newtonian

122 INDIAN J. ENG. MATER. SCI., JUNE 1999

behaviour of the solid liquid mixture were measured by using a Weissenberg rheogoniometer at various concentration levels. The specific gravity of the material is 2.82 and the static settled concentration was measured as 58 .67% by weight. The particle size distribution of the solid material which shows fairly well graded distribution with approximately 50 % particles being finer than 75 microns. The measurement of relative viscosity of slurry at different solid concentrations indicates (Table I) that the slurry exhibits Newtonian character over the solid concentration range used.

Experimental Procedure and Data Analysis At any given solid concentration, the differential

pressure across the venturi meter the corresponding flow rate were measured at different flow velocities. Similar data was obtained at different solid concentrations . The velocities of slurry flow in the pipe loop during the present investigation were varied in the range of 0.6 to 2.0 mls for different solid concentrations in the range 3.4-31 % by wt.

From the measured vakIes of differential pressure and the flow rate, the discharge coefficient of the venturi meter has been calculated, using the equation given below:

where, At is the area of cross-section of

venturi meter throat, (m2), A is the area of cross­

section of pipe, (m\ Cd is the di scharge coefficient,

Q is the flow rate of slurry, (kgls), /:!p is the differential pressure, (N/m2), ps is the density of

.. o

! ·0r------------------,

u 0'8 .. a-D .c

~ 0·7 o I OWlteordat-o . ; Cw:~.4 '/ , v Cw:8-44 '/;]

~W:15)4'1. x Cw=24 .0'l. OCw:]1·0'!. 0'6 L-__ - __ -Lt _-_-_-_-_--Lt- ·_-~_-_-_-_-Lt-_--~~_- ~IL ___ ..J

o 2 3 4 Ve locit y • m/s

Fig. ~()enicient of discharge of the eccentric venturi meter with elongated th roat with water at various concentrations and slurry flow ve locities

slurry, (kglmJ) and ~ is the equivalent diameter ratio

(~) At each flow rate, the Reynolds number is also

calculated. The coefficient Cd has been evaluated from the measured value of flow rate and differential pressure. Dependence of Cd on flow velocity, solid concentration and solid properties has been established and discussed.

Results and Discussion Measurements have been made with the modified

venturi meter with water and slurry at five different solid concentrations. The results are presented in Figs . 3-6.

Variation of discharge coefficient for water

Fig. 3 shows the variation of discharge coefficient for water with flow velocity. It is seen that venturi meter coefficient remains constant for the range of velocities tested and has an average value of 0 .9096. This value is appreciably lower than that for a conventional venturi meter. This can be attributed to the fact that the convergence in the modified venturimeter is not ax i-symmetric and hence the losses due to secondary flows are some what higher.

Variation of discharge coefficient with solid concentration

Fig. 3 also shows the variation of discharge coefficient at different solid concentrations with flow velocity. It is observed that the maximum deviation of 3.5% in di scharge coefficient is at the maximum solid concentration tested. It is also seen that at any given solid concentration, the variation in the measured values of disc harge coefficient at different flow

1 .0r-----------·~----_ _,

'" u . ~

" . ~ 0.9 u

-.. o u

.. ~ ~ 0.8

~ ,,'--_-'-__ .L.-_-'--__ <--_---"­o 5 10 20 30

Cw,'!. by wI

Fig. ~oefticient of discharge of the eccentric venturi meter with elongated throat at different concentrations of slurry

BHARANI et at.: PERFORMANCE CHARAClERISllCS OF AN ECCENTRIC VENTIJRIMETER 123

o ......

\.()

0-8

0·6

0 ... a o V.0.78 m/s +- V;\ ·28m/s eV-1.8) mlS

o + D

0 +0 )- 0.4 f-

D ...... )-

D ....... )-

0 · 2

o o

1.0

0.8

0.6

0.4

0·2

o 04

1· 0

0 ·8

0.6

0.4 -

0·2

0·5

0+

0.6

OYrO.9) m/s ... V;I . 23m/s OY=l.Ijom/s

o I 1

D

+0

\.()

Cw/C_ff

0

+0 0

+0

0

0+ 0

0+ 0

o c

CI-!- 0

0+ 0

I

\·S

oY=1.0lm/s +V-I.48m/s DY=1.89 m/s

0

+ 1

1·2

C 0

o ... 0

I I I 1

0.4 O ·~ 0-' 0·' 0.8 0.9 1.0 1.1 1·2 1·) Cw/Cw~tt

~ .o

0

1·6

1.4

Fig. 5-Concentration distribution along vertical plane in straight pipe, at various efflux concentrations and flow velocities (a) CwcrF 3.4 %, (b) Cwen'" 15.3 %, (c) Cwerf= 3 1.0 %

velocities is within ± 0.3%. Similar phenomena was observed by Seshadri and Singh' for a conventional venturi meter when used with solid-liquid mixtures.

To bring out the effect of solid concentration on discharge coefficient, the average value of discharge coefficient has been calculated at each solid concentrati on and its variation has been plotted in Fig. 4 . It is seen that average value of discharge coefficient increases marginally with solid concentration till a concentration of 15% by weight and thereafter it remains almost constant. The inc rease in discharge coefficient is marginal and the increase is fou nd to be on ly 3.5% even at the highest solid concentration tested . This increase can be

1.0

~ 0 Y-O·78 m/~ l ' 0.8 + Ya'·28m/s

C Yal63m/ s 0 .+ a

0.6 0 + 0

0 ...... o • >- 0.4

0·2 a + 0

a + 0

0 0 0.5 1·0 1· 5 2 ·0

C'1Cw~ft

1·0

I oYcl.D1mjS \ 0.8 + V c 1.1.8",,5

OV% U!gm/S 0 + 0

0.11 0 + 0

0 a + 0 -- 0,4t->-

0'2 a + 0

a -+ 0

0 0·6 0·8 1·0 1· 2 I. '

Cw/Cw.ft

1· 0

~ OV-o.93m/Sj 0·8 +V-l.23 mls

oV=I.60m/s ( - 0

0.6 -iu:l 0 -->- • 0

0.4

0 ·2 0+ 0

0+0 oL-__ -L ____ L-__ -L __ ~ ____ ~ __ ~

0.6 0·7 0·8 O·g 1·0 1·1 1'2

Cw/Cwfff

Fig. &-Concentration distribution along vertical plane at ventu ri meter throat, at various efflux concentrations and fl ow velocities (a) CwelF 3.4 %, (b) Cwer!'= 15.3 %, (c) Cwd1'" 3 1.0 %

attr ibuted to reduction in losses at low solid concentration due to suppression of turbulence 10. At high concentration, reduction in loss is compensated by increased viscosi ty of the mixture. From the above results, an average value of discharge coefficient can be ca lcu lated wh ich could be applicable at all concentrations with an error band of ±1 .75%.

Solid dis tribution pattern

In order to ge t an insight into the effect of the ven turi meter on the overall solid distribution field, the concentration di stribution was measured along the vert ica l plane of the pipe much downstream of the meter and at the throat. The measured values of

124 INDIAN 1. ENG. MATER. SCI., JUNE 1999

concentrati on in the pIpe and the modified venturi meter throat a re given in Figs Sand 6. It is observed th at the concentration profiles in the pipe are skewed with maximum solid concentration being c lose to the bottom (Fig. Sa-c). Further, it is also obse rved that at a g iven concentration of solid materi a l, increase in flow rate brings more uniformity in the concentration profile and it is in agreement with the reported trends lO

. This trend is seen at all va lues of so l id concentrations. Fig. Sa-c also show th at at any given flow rate increasing solid concentrati on also increases uniformity in the solid distribution.

Solid distribution at the throat is shown in Fig. 6a-c. The effec t of fl ow velocity and solid concentration on the loca l concentration di stribution is similar to the pipe, i.e., concentration profile becomes fl atte r with increase in the discharge rate and the efflu x concentration .

A compari son of concentration profiles at an efflux concen trati on of ].4 % at different di scharge rates shows that at any g ive n di scharge rate, the concentrati on profi Ie is flatter at the throat as compared to the pipe. This is expected because of increased ve loci ty at the throat would make the suspension more homogeneous. However, flow still remains in the he te rogeneous regime only unlike the conve nti onal venturi meter where strong redistribution

of solid partic les take place. Thus, the flow di sturbances created by modified venturi meter a re much less as compared to the conventional venturi meter.

Conclusions Detailed ex periments on the modified venturi meter

has revealed its suitability for fl ow metering application in two phase flow s. The main conclusions of thi s study are as follows:

I The value of di scharge coefficient of modifi ed venturi meter is some what lower as compared to conventional venturimeter.

2 The effect of flow ve locity on the value of di scharge coefficient is marginal over the range of ve lociti es .fQr -which experiments have been performed. Hence, we can assume Cd to be a constant.

3 The di scharge coefficient of the modified venturi meter JIl c reases marginally with so lid

concentrations upto IS % concentration by wt. and thereafter remains constant with increase in solid concentration. However, the variation of Cd over the solid concentration range of 0 to 31 % by wt. is only 3.S% and hence we may be able to use an average value based . on water data for metering of slurries if high accuracies are not required.

4 The modified shape of the venturi meter throat does not alter the distribution pattern of the solids compared to a conventional venturi meter. The flow patte rn in side the modified venturi meter remains heterogeneous at moderate flow veloc ities and efflux concentrations.

Nomenclature Cv = concentration of solids (by wt.) Cwel l = efflux co ncentration (by wt.) d diameter of the throat of conventional venturi meter,

m

D diameter of pipe, m (Ie equivalent diameter of the throat of the modified

venturi meter, m H height of the elongated throat, m Y = distance along the vertical plane from the bottom of

pipe/venturi meter, m

References I Seshadri V & Singh S P, Flow MeaslIrement in SilIrry

Pipeline using Venlllrimeter, Proc. of 14th National Conf. Fluid Mechanics & Fluid Power, 1986, V /33-39 .

2 Sharma M P. NlImericai and Experimental Study of Gas­Particle Flows in Orifice alld Ven llIries, Ph. D Dissertation, Washington State Uni versi ty, USA, 1977.

3 Lee J, Scaling La ll 's fo r Melering the Flow of Gas Particle SlIspension throllgh VenllIries, Ph.D Dissertation, Washington State Un iversity . USA, 1980.

4 Payne A L & Cro+we C P. Metering the Mass fl ow of Gas Solid Mixtllres ill NOll Standard Vel1ll1ri COllfigllratioll, Proc Symp Instrument Control of Fossil Energy Processes, New Cavalier, Virginia, June 9- 12, 1980,557-564.

5 Graf W H, 1 Hw lralll Res, 5 (1967) 161. 6 Brook N, Proc Ill st Mech El1 g, 176 ( 1962) 127. 7 Hasan R. Baria D N & Chaudhary N M, Ligl1iie -Water Slurry

Flow Measllrement lIsing a VenllIrimeter, Proc. Symp. on Intrumcn tati on and Contro l Fossil Energy Processes, 1982, 458-464.

8 Abbas M A & Crowe 0 T, 1 Pipelin es, 4 ( 1984) 143.

9 Hirata Y. Tak 'lIlo M & Narasaka T, l SME Jnt . 1, Series-B, 38 ( I ()95) 4'+0.

10 Mishr'l R. S/i((lil'.\· IIntil l'.fiow O{IIIII Ili sized particlliate solid­/iqllid lIIixllln's in /wri:o/lllli /Jipe/ines, Ph. D Dissertation, India n Ill'.titlitc of Technology. Delhi . Indi a. 1 ~96.