Experimental Study of a Simple Nozzle Flow Meter with Various Diameter Ratio

Ainul Ghurri, AA Adhi Suryawan, SPG Gunawan Tista

Mechanical Engineering Department, University of Udayana

Kampus Bukit Jimbaran, Bali, Indonesia

Email: a.ghurri@gmail.com

ABSTRACT

Experimental study of nozzle flow meter was conducted by using nozzle having diameter

ratio β = 0.5, 0.6, and 0.7, respectively at Re = ± 5000 ÷ ± 31000. The shape of the nozzle is

similar to orifice plate at reversed position. Water is circulated through nozzle flow meter.

The theoretical capacity was determined by using the mass conservation and Bernoulli equations based on the measured pressure at upstream and downstream of the nozzle. The

actual capacity was measured by using V-notch weir and sight glass. The results showed that the values of Cd have trend line which is like the common nozzle flow meter, i.e. increase

with Reynolds number. Nozzles with diameter ratio 0.7 and 0.8 resulted in the effective value of Cd. Unfortunately, the lowest value of irrecoverable pressure drop is still high, i.e. 50%-

45%.

Keywords: Nozzle, flow measurement, coefficient of discharge, pressure drop

1. INTRODUCTION

One of the most commonly used device for flow measurement in industries is

pressure differential flow meter (Sondh et.

al., 2002). In a conventional pressure differential flow meter, the differential

pressure measured across the orifice plate, nozzle or venturi indicates the flow rate.

Compared to orifice meter, the nozzle has a lower head loss. In many applications, this

additional loss due to the flow meter is not desirable and the need for an alternate type

of metering device arose. This paper

reported the experimental study of a simple

nozzle having shape as reversed-orifice

plate. The results were then compared to the

literatures of nozzle flow meter to conclude

whether this simple nozzle can represent the

nozzle meter. Very little information is

available on the nozzle meter caused the

literature review below is in related to the

orifice flow meter.

Morrison et.al. (1995) investigated the

response of orifice flow meter due to a flow

disturbance at the upstream. The results show that the pressure distribution does not

change with varying axisymmetric flow distortions. On the other hand, the pressure

distribution is very dependent upon the

swirl. Prabu et.al. (1996) and Zimmermann (1999) used a similar disturbance i.e. single

and double bend to examine the changes of

coefficient of discharge (Cd) the orifice meter. The data show that the orifice meter

is more sensitive to upstream disturbance than the conical flow meter. Zimmermann

recommended a correction to ISO 5176 (Measurement of fluid flow by means of

pressure differential devices, 1991), i.e. to reduce the required minimum straight length

at the upstream of installed orifice flow

meter. Ramamurti and Nandakumar (1999)

investigated the separated flow, the

separated flow followed by attachment, and

the cavitated flow through the small orifice

plate. The result show that the Cd changed

significantly due to the separated and the

cavitated flow. All of the previous research

used the sharp-edged orifice plate.

Kim et.al. (1997) examined the effect of

orifice plate thickness on small diameter

ratio orifice meter. The tested orifice plate

had t/d = 0.55 and 0.7 where t is orifice plate thickness, d is orifice plate diameter. The

trends in the results for thickness effect were not conclusive and could be attributed to

edge sharpness. Fossa and Guglielmini

(2002) tested the pressure drop on single

and two phase flow across the thick and thin

sharp-edged orifice plate. The diameter ratio

(β = d/D, where D is pipe diameter) used in

this experiment were 0.73 and 0.85

respectively. The thick orifice plate had t/d

= 0.59. The results of single phase flow

show that the pressure drop the thicker

orifice plate was higher than the thinner (t/d

= 0.03 and 0.2).

Ghurri and Nata (2006) reported that the

position of pressure tap at upstream and

downstream of orifice plate had an

importance effect on the flow measurement.

The different position resulted in different

measured pressure, and then the different theoretical capacity too. The recommended

position of pressure tap is the position which resulted in the consistent changes of

theoretical capacity compared to the actual capacity.

The present research is aimed to investigate the effect of diameter ratio on

the Cd changes, and to examine whether the use of reversed orifice plate as nozzle will

has Cd characteristic like common nozzle

flow meter. 2. FLOW THROUGH A NOZZLE

Figure 1 shows the model of an ideal

nozzle in a pipe. In the present study, a

nozzle that exactly same with sharp-edge

orifice plate but in reversed-position was

installed to flow a fluid as shown in Fig 1. It

could be assumed that between sections 1

and sections 2 there is a flow without

friction. The pressure differential between

1 and 2 can be determined by means Bernoulli equation.

Figure 1. Ideal nozzle flow in a pipe

By assuming that the flow is horizontal

at constant elevation, Bernoulli equation

became:

P1 + 1/2 ρ V12 = P2 + 1/2 ρV2

2 (1) Where

P = Pressure (Pascal)

ρ = Fluid density (kg/m3)

V = Velocity (m/s)

We needed to assume that the velocity

profile is uniform at upstream and

downstream, and then the theoretical

capacity (volumetric flow rate) can be

formulated as:

Qth = V1 A1 = V2 A2 (2)

Where

Qth = Theoretical volumetric flow rate

(m3/s) A1 = Cross sectional area at 1 (m2)

A2 = Cross sectional area at 2 (m2) By substituting V1 of equation (1); we

obtained the new formula of equation (2):

Qth = A2 ( )

21

2

1

2

21

1

2

−

−

A

A

PP

ρ

= 2

4d

π ( )

21

4

21

1

2

−

−

D

d

PP

ρ

(m3/s) (3)

It is defined diameter ratio β = d/D; then the

equation (3) changed to:

ρπ

β

PdQth

∆

−=

2

41

1 2

4

(m3/s) (4)

Thus the theoretical capacity can be

determined by measuring the pressure

differential (∆P) between section 1 and

section2. We can examine the accuracy of

the flow measurement devices by comparing

the actual to the theoretical capacity. The

ratio of actual to theoretical flow capacity

was known as coefficient of discharge, Cd:

th

actd

Q

QC =

(5)

V1

P1

V2

P2

V3

P3

Flow without friction

Bernoulli

Flow with losses

d D

1111 2222 3333

3. EXPERIMENTAL APPARATUS The experimental set up is shown in

Figure 2. Water was circulated by means a

pump (2). The volumetric flow rate can be

simply controlled by a valve (6). During the

water flew through the nozzle (7)

manometer will measure the pressure at

upstream and downstream of nozzle. The

pressure measurement was conducted at

some upstream and downstream points. The

fluid was discharged to a V-notch weir

whereby the actual capacity can be obtained.

There was a sight glass in this experimental

apparatus as other way to measure the actual

capacity.

Figure 3 (b) shows the nozzle used in

present study which is exactly same with the

orifice plate (Fig. 3(a)) in reversed-position.

The geometrical data and flow condition

were:

- The pipe was acrylic transparent, 16

mm inner diameter

- The nozzle have diameter ratio β =

0.5, 0.6, 0.7 and 0.8, respectively.

- The nozzle thickness was 30 mm.

- The pressure tap positions were 25.4

mm at upstream and downstream of

the nozzle respectively.

Reynolds number ranged between ±

5000 and ± 31000.

Figure 2. Experimental set up

Figure 3. (a). Orifice flow meter (b). Nozzle flow meter

1. Test section base

2. Pump

3. Water tank

4. Suction line

5. Valve at by pass line

6. Valve at discharge line

7. Nozzle

8. Manometer 9. Manometer board

10. V-notch weir

11. Sight glass

12. Secondary water tank

13. Valve

d

P1 P2

D Flow

P1 P2

d D

4. RESULTS AND DISCUSSION 4.1. Ratio of actual capacity (Qact) to

theoretical capacity (Qth)

Figure 4, 5, 6, 7 show changes of Qact

and Qth the tested nozzle flow meter for β =

0.5, 0.6, 0.7 and 0.8, respectively. Qth of

nozzle with β = 0.5 was greater than the

Qact. The difference between Qth and Qact

decreased for β = 0.6 and 0.7 at low

Reynolds number. The contrary condition

was shown for β = 0.7 at higher Reynolds

number and β = 0.8 wherein Qth was smaller

than Qact. This can be attributed to the flow

phenomenon at vena contracta where the

fluid may be accelerated very efficiently.

After acceleration, it was very difficult to

slow down (decelerate) the fluid efficiently.

Thus, the extra kinetic energy of the fluid

was partially lost because of viscous

dissipation, so that the pressure does not

return to the ideal value. These losses

couldn’t be accommodated by the equation

of Qth that derived from Bernoulli equation

for ideal flow.

The coefficient of discharge (Cd) were

then plotted (in Figure 8) based on the Qact

and Qth according to the equation (5).

Figure 4. Qact vs Qth Nozzle Flow Meter with β = 0.5

Figure 5. Qact vs Qth Nozzle Flow Meter with β = 0.6

0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

2.50E-04

3.00E-04

3.50E-04

4.00E-04

4.50E-04

5.00E-04

5.00E+03 7.50E+03 1.00E+04 1.25E+04 1.50E+04 1.75E+04 2.00E+04 2.25E+04 2.50E+04

Reynolds number (Re)

Ca

pac

ity

(m

3/s

)

Qact Qth

0.00E+00

1.00E-04

2.00E-04

3.00E-04

4.00E-04

5.00E-04

6.00E-04

7.00E-04

5.0E+03 7.5E+03 1.0E+04 1.3E+04 1.5E+04 1.8E+04 2.0E+04 2.3E+04 2.5E+04 2.8E+04 3.0E+04

Reynolds number (Re)

Ca

pa

cit

y (

m3/s

)

Qact Qth

Figure 6. Qact vs Qth Nozzle Flow Meter with β = 0.7

Figure 7. Qact vs Qth Nozzle Flow Meter with β = 0.8

Figure 8. Cd Nozzle FM at various β

0.00E+00

1.00E-04

2.00E-04

3.00E-04

4.00E-04

5.00E-04

6.00E-04

5.0E+03 7.5E+03 1.0E+04 1.3E+04 1.5E+04 1.8E+04 2.0E+04 2.3E+04 2.5E+04 2.8E+04 3.0E+04 3.3E+04

Reynolds number (Re)

Cap

acit

y (

m3/s

)

Qact Qth

0.00E+00

1.00E-04

2.00E-04

3.00E-04

4.00E-04

5.00E-04

6.00E-04

5.0E+03 1.0E+04 1.5E+04 2.0E+04 2.5E+04 3.0E+04 3.5E+04

Reynolds number (Re)

Cap

acit

y (

m3/s

)

Qact Qth

0.6

0.8

1

1.2

4.00E+03 9.00E+03 1.40E+04 1.90E+04 2.40E+04 2.90E+04 3.40E+04

Reynolds number (Re)

Cd

ββββ = 0.5

ββββ = 0.6

ββββ = 0.7

ββββ = 0.8

Figure 9. Coefficient of Discharge Nozzle FM (Munson, 2002)

Figure 8 show that the Cd increased as

the Reynolds number. These were exactly

the characteristic of nozzle flow meter (see

Figure 9). Cd values > 1 can be accepted as

published by few of literatures (Fox, 1994;

Kim et.al., 1997). Water Resources

Research Laboratory (2001) reported that

the effective Cd value of nozzle flow meter

is about 0.96 ÷ 1.2. So we can conclude that

the simple nozzle having shape as reversed-

orifice plate could represent a nozzle flow

meter.

4.2. Irrecoverable Pressure Drop

Figure 10 below show the pressure

distribution along upstream to downstream

of the nozzle with β = 0.7. Zero (0) of the X

axis represented position at the nozzle; -1

and -2 are at upstream; 1, 2, 3, 4 are at

downstream. Q1, Q2, Q3 … were the

increasingly flow capacity. The

irrecoverable pressure drop was head loss

due to the measurement device. The

maximum and irrecoverable pressure drop

of each flow capacity was sketched in

Figure 10. The irrecoverable pressure drop

was an important consideration for the use

of pressure differential flow meter; and

appeared as percentage of maximum

pressure drop. As shown in Figure 11, the

percentage of irrecoverable to maximum

pressure drop decreased at the higher

diameter ratio (β); and slightly decreased

with the Reynolds number. The percentage

of irrecoverable to maximum pressure drop

of the nozzle with β = 0.8 was about 50%-

45%. This was still higher than the previous

work (Ghurri & Nata, 2006) that using a

thick orifice plate with bevel. At the

previous research the irrecoverable pressure

drop reached 40%-30% for the orifice with

β = 0.6 and 0.7 (Ghurri & Nata, 2006).

Figure 10. Pressure distribution along Nozzle Flow Meter with β = 0.7

Figure 11. Irrecoverable pressure drop as percentage of maximum PD

5. CONCLUSION The experimental study of nozzle flow

meter was conducted by using simple nozzle

having shape as reversed-orifice plate with

diameter ratio, β = 0.5, 0.6, 0.7, and 0.8 at

Reynolds number ±5000 to ±31000. The

conclusions were obtained as follow:

1) The Cd value had characteristic as

common nozzle flow meter, i.e.

increased as the Reynolds number

increased.

2) The Cd of nozzle with β = 0.7 and 0.8

can be categorized as the effective value.

-2.50E+03

-2.00E+03

-1.50E+03

-1.00E+03

-5.00E+02

0.00E+00

5.00E+02

1.00E+03

1.50E+03

2.00E+03

2.50E+03

3.00E+03

-3 -2 -1 0 1 2 3 4 5

Posisi Pressure Tap

Tekan

an

( P

ascal

)

Q1 Q2 Q3 Q4 Q5 Q6 Q7

Q8 Q9 Q10 Q11 Q12 Q13

40%

45%

50%

55%

60%

65%

70%

75%

80%

4.00E+03 9.00E+03 1.40E+04 1.90E+04 2.40E+04 2.90E+04 3.40E+04

Reynolds number (Re)

Irre

co

ve

rab

le P

ress

ure

Dro

p (

% o

f M

ax.

PD

)

Irreco

vera

ble

pre

ssu

re

dro

p M

axim

um

pre

ssu

re d

rop

ββββ = 0.5

ββββ = 0.6

ββββ = 0.7

ββββ = 0.8

Pressure tap position

Pre

ssu

re

(Pa

scal)

3) The lowest percentage of irrecoverable

to maximum pressure drop reached

during experiment is still high enough

i.e. 50%-45%.

ACKNOWLEDGMENT The authors thanks the Ministry of Research,

Tech., and Higher Education of the Republic

of Indonesia and LPPM University of

Udayana for supporting this research and

paper through Hibah Bersaing Grant 2013-

2015.

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