Baker R.C. Flow Measurement Handbook: Industrial Designs, Operating Principles, Performance, and Applications

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5.B DEFLECTION OF ORIFICE PLATE AT HIGH PRESSURE

107

TEFLON SEAL (SEAL

HETALSEAL (SEALNo

DIRECTION

FLOW

OIRECTION

FLOW

DIRECTION

FLOW

CTRINGS

METAL

SEAL (SEAL No

Figure 5.7. Differential seal ring arrangements (from Fulton et al. 1987 repro-

duced with permission of the authors, the Norwegian Society of Chartered

Engineers, and Christian Michelsen Research).

The original research was carried out at the British Gas Research Station in

Killingworth, England. It used plates rigidly mounted between flanges and tested

at differential pressures between 0 and 120 mbar.

Fulton et al. (1987) undertook further tests to determine the effect of seal ring

mountings as shown in Figure 5.7 and differential pressures up to 1000 mbar. Their

results appear to suggest that the deflection with the Teflon seal ring was generally

about 15% greater than the values from Jepson and Chipchase's (1975) formula,

whereas the results for the No. 1 metal seal were close or about 20% less and for the

No.

2 metal seal were close or about 30-40% less.

Simpson (1984) provided a useful digest of the papers by Norman et al.

(1983,

1984) in which this problem has been developed and experimental work undertaken

to validate the results. Simpson suggested that Norman et al.'s equation (essentially

108

ORIFICE PLATE METERS

that in

1042: Sect. 1.5: 1997)

— Ci I

(5.13)

where

mass flow rate

differential pressure across the plate

elastic modulus of plate material

D = orifice plate support diameter

thickness of orifice plate (=E in Figure 5.3, following ISO 5167)

could have simpler expressions for a\ and

than given by Norman et al. because

the plate thickness will usually be fixed by the next most appropriate thickness of

material. Simpson, therefore, gave (as in the standard)

fli =0(0.135-0.1550)

d = 1.17-1.O60

To avoid plastic deformation, the differential pressure must be below

6(0.454-0.4340)

(5.14)

where

Metering

error

Slope

0.2

0.1

= yield stress for plate material

0 = orifice plate diameter ratio d/D

With Equations (5.13) and (5.14), it is possible to design for an error of, say, not

more than

0.1%

for a certain working pressure and for safe operation without plastic

deformation with fault conditions of flow

and differential pressure drop.

For a working differential pressure of

up to 500 mbar (and up to 1000 mbar un-

der fault conditions without yielding) for

0 = 0.4 with 304S.S plate material having

= 195.4 x 10

Pa and a

= 215 x 10

Pa,

Simpson obtained values of

h/U > 0.016 for required maximum

error

h/D' > 0.014 to avoid plastic deforma-

tion

h must, therefore, be equal to or greater

than 0.016D'. It should be noted that,

in extreme cases of high differential pres-

sure,

the allowed thickness according to the

Figure 5.8. Metering error due to initial lack of plate

flatness (from Simpson 1984; reproduced with per-

mission of the Institute of Measurement and Control).

5.7 EFFECT OF PULSATION 109

standards may be exceeded in meeting these plate bending requirements. The stan-

dard also implies that a safety factor on a

(of three) is a wise precaution.

Figure 5.8 gives curves for errors due to flatness slope against p ratio.

5.7 EFFECT OF PULSATION

In considering the installation of a flowmeter, the assumption is usually made that

the flow is steady. In many cases, this is probably a fair assumption. However, there

are situations when it is not the case (e.g., when a reciprocating compressor, an

internal combustion engine, or some form of rotary valve is in the line). It is often

very difficult to decide whether the flow is indeed steady or pulsating in some way.

We might idealize the pulsating flow as consisting of a sinusoidal ripple super-

imposed on a steady flow. This idealization is probably seldom valid, and little will

actually be known about the amplitude, frequency, or flow profile. Mottram (1992,

cf. BS 1042 Section 1.6, which uses some of his work), after the wise comment, "If

you can't measure it, damp it!" made some additional useful points.

• If the frequency is above about 2 Hz, differential pressure transducers will, gen-

erally, be too heavily damped to pick it up. (Transducers with a response up to 2

kHz or more are likely to be specified and to be more expensive.)

• The standard describes some detection techniques including the use of a thermal

probe to sense the presence of pulsation.

• Some flowmeter signals show indication of pulsation.

• In some cases, the error may be deduced from the raw flowmeter signal.

• Connecting leads in differential pressure meters can cause resonance and con-

fusing effects.

The orifice plate meter is affected by pulsation, and so it is necessary to reduce

the pulsation and to have an idea of the error likely from any residual pulsation.

The effects of pulsation on an orifice meter are:

a. Nonlinear

(square root)

error.

If a signal is averaged to obtain a mean flow, it is

necessary that the instantaneous flow be proportional to the signal. If this is not

so,

an error will be introduced.

Inertia

error.

If the fluid does not follow the changes in the flow rate instanta-

neously, an error due to the inertia of the fluid will result.

Velocity profile

effect This effect is a result of the change in profile from fully

developed to the unsteady flow.

Resonance.

Resonance occurs because some component of the system is resonat-

ing at the pulsation frequency.

e. Limitations in the

pressure measurement

device.

If the pressure measurement device

does not respond correctly to pulsating flow, the pressure measurement may be

incorrect.

Of these, the most important are (a), (d), and (e), the last two of which are

related. The latter two are particularly possible in the connecting tubes between the

110 ORIFICE PLATE METERS

flow tube and the transducer, and because of the rate of response of the transducer.

A manometer will possibly be of little value in an application with pulsation.

Thus for (a), Gajan et al. (1992) reviewed work that showed that, for quite high

values of the ratio of rms fluctuating pressure difference to steady pressure difference,

up to 0.5 at least, the main error is due to the square root effect and can be eliminated

with a high speed response transducer. Even with a slow response transducer, the

error for the ratio, if within

0.1,

may be within about 1%.

Botros et al. (1992) looked at (d) and (e) and found that the combination of lines

and transmitter form a resonator that can amplify or attenuate. They recommended

that very short lines of essentially constant diameter and a transmitter with a small

volume and a high frequency response should be used.

Commercially available differential pressure transmitters are generally unsuit-

able for dynamic measurement (Clark 1992). The dynamic response of differen-

tial pressure transducer systems is significantly affected by length of transmission

line and whether the measurement medium is liquid or gas. Gas and liquid lines

appear to be susceptible to oscillations, and in liquid systems there is a need for

proper gas venting arrangements. Considerable care is required in order to make

reliable dynamic measurements particularly when using a liquid medium (Clark

1992).

The square root problem is shown by

\ f

JKpdt<

I- f

Apdt

(5.15)

t Jo

A transducer with pressure connections that is capable of responding within a time

that is short compared with the period of the fluctuation, and the signal of which

is square-rooted immediately and then averaged, will give the correct average value.

This is essentially the left-hand side of the inequality (5.15). On the other hand,

if the pressure is averaged and then the square root is taken, this is essentially the

right-hand side of the inequality and the apparent flow rate will be high compared

to the actual flow rate. Mottram's (1981) results for pulsation error are shown in

Figure 5.9(a), and they suggest that the experimental results confirm the dominance

of the square root error when compared with errors (b) and (c). However, Mainardi

et al. (1977) appeared to suggest that (b) and (c) cause a change in the coefficient so

that the effect of pulsation for a fluctuating ripple of 6% of the mean flow will cause

an error if pulsation is measured with a high frequency response transducer of 1.5%,

whereas the error is 4% for a 15% ripple. (Frequencies appeared to be up to about

50 Hz.)

Williams (1970) identified the possible sources of error when manometric devices

are used to indicate mean differential pressure in a pulsating flow as

• wave action and resonance effects in the connecting leads,

• volumes of ducts of varying section within the manometer and leads, and

• restrictions in the leads, which cause a nonlinear relationship between flow and

pressure drop and result in nonlinear damping.

The effect of pulsation on a manometer is shown in Figure 5.9(b).

5.7 EFFECT OF PULSATION

111

LLJ

'\theoretical

square root

(a)

03 04 05 0-6

rms PULSATION AMPLITUDE

MEAN DIFFERENTIAL PRESSURE

07 08

LLJ

(b)

-1-0

-20

o- sine

- non-sine

A A

)

O O^ OQ

ooo°

5>A

O A

°T

° A

^ A

§ \

kjO

° o°

OO A O^

A A

O A

_O°_A|

O—

0-1

0-2 0-3 0-4

0-5 O0-6 0-7

rms PULSATION AMPLITUDE A

MEAN DIFFERENTIAL PRESSURE

Figure 5.9. Effect of pulsation on pressure measurement (from Mottram 1981;

reproduced with permission of the author and of the Instrument Society of

America): (a) Total error at low pulsation amplitude; (b) U-tube manometer

error.

Before leaving the subject of pulsation effects, it is important to include a further

note (cf. Section 2.6) on the Hodgson number:

(5.16)

where V is the volume of pipework and other vessels between the source of the

pulsation and the flowmeter position (Figure 2.5), Ap is the pressure drop over the

same distance, f is the frequency of the pulsation, q

is the volumetric flow rate,

and p is the absolute line pressure. With this number, it is possible to plot curves to

show the likely error levels for various values of H. Oppenheim and Chilton (1955)

112 ORIFICE PLATE METERS

0.2 0.3 0.4

Hodgson Number, H

Figure 5.10. Hodgson's number, (a) Pulsation er-

ror curves for a triangular pulsation of varying

amplitude (from Oppenheim and Chilton 1955;

reproduced with permission of

ASME).

(b) Com-

parison between Hodgson's number and experi-

mental results (from Mottram 1989; reproduced

with permission of Elsevier Science).

10.0

6.0 -

4.0 -

2.0 -

Experimental results

-O Sinusoidal

• Non-

_ sinusoidal

•

- D <

2r#-HI

]

°a

Frequency r«

V IV -

O.E

\ Theoretical curve, equation (5.20)

a \

° V

•

^•

B°ao^5

^—.

jnge 5-50 Hz

(b)

0.01 0.1

1.0 10.0

have given plots of error levels for various types of flow. In Figure 5.10(a), one such

set of curves is shown.

Mottram (1989) suggested that an expression for the total error in the indicated

flow rate of a differential pressure flowmeter is

which for small amplitude ratios can be written as

vms

= V

(5.17)

(5.18)

5.8 EFFECTS OF MORE THAN ONE FLOW COMPONENT 113

where V is the mean velocity and

rms

is the rms value of the unsteady velocity fluc-

tuation in the pipe. He then suggested that if

maximum allowable percentage error

is 0 where

</>

= 100£

, and using the criterion for damping in Equation (2.14), then

H 1 (WtQud

(

where subscript ud implies undamped and y is the isentropic index for the gas or

H (Wfod

(5<20)

y ~ V0

where K = 10/(4\/27r) = 0.563. He claimed that experimental evidence is available

to validate the safety of this criterion provided the flow pulsation amplitude can

be measured. Some of Mottram's (1989) data compared with Equation (5.20) with

K =0.563 is shown in Figure 5.10(b). Where estimation is necessary, he suggests a

safety margin by using K =

This appears to be confirmed by the data that Mottram

(1989) included in his paper (cf. Sparks et al. 1989 who emphasized the problems

and the only safe solution - the removal of pulsation).

5.8 EFFECTS OF MORE THAN ONE FLOW COMPONENT

Attempts have been made to relate the differential flowmeter equation to the data for

flow of a fluid mixture, most commonly steam, through the orifice. The attempted

adjustments have followed three approaches:

1. Adjusting the value of density to reflect the presence of a second component (cf.

James 1965-6);

Adjusting the discharge coefficient to introduce a blockage factor for the other

components, expressed as a function of the dryness (cf. Smith and Leang 1975);

Relating the two-phase pressure drop to that which would have occurred if all

the flow were passing either

a gas or

a liquid. The ratio of two-phase pressure

drop to liquid flow pressure drop <I>j?

is equated to a function of x, the dryness

fraction.

Miller (1996) favored the third approach as being the easiest to use. It has also

been investigated by several workers, and various expressions for

<&j

have been

tabulated by Grattan et al. (1981) from the work of Chisholm (1977), Collins and

Gacesa (1970), James (1965-1966), and Watson et al. (1967). For other references,

the reader is referred to Baker (1991a).

The main reservation concerning some of these correlations relates to whether or

not they can be applied to different pipe geometries, fluids, Reynolds numbers, etc.

Steam

Grattan et al. (1981) gave experimental pressure loss data for orifice tests with an

empirical curve:

<$>l

= 1.051 +

291*

- 3,796x

+ 74,993x

- 432,834x

for 0.00005 < x < 0.1 (5.21)

114 ORIFICE PLATE METERS

100

0.0000!

0.0001

0.001

Mass dryness fraction x

0.01

Figure

5.11.

Experimental pressure loss data for orifice tests (from Grattan et

al.

1981;

reproduced

by permission of

NEL).

and this is shown in Figure 5.11. The scatter is an indication of the limited value of

such an empirical curve and of attempts to predict flowmeter performance in two-

phase flows. Rooney (1973) also obtained values for the parameter

4>^

(cf. Chisholm,

1967;

Chisholm and Leishman, 1969; Chisholm and Watson, 1966).

Owen and Hussein (1991) pointed out that if the water content was very small,

the droplets would probably have a negligible effect on the flowmeter response,

and so the mass flow should be corrected to allow for the mixture density rather

than the vapor density. For wet steam of dryness x greater than about 0.9, this

correction is approximately F = 1/x. Owen and Hussein compare this value with

other corrections in Figure 5.12(a). Note that y is the wetness fraction. In particular,

BS 3812 suggested

and the

Shell Flowmeter Engineering Handbook

proposed

F =

1.74-0.74*

for x> 0.95

(5.22)

(5.23)

Hussein and Owen (1991) referred to two correlations: James's giving a correction

factor of

F =

1/2

and Murdock's

F =

1.26(1

(5.24)

(5.25)

Figure 5.12(b) for seven alternative correlations suggests that the data scatter around

those of James and Murdock. Hussein and Owen (1991) showed that pressure had

little effect on correction factors, and that the

Shell Flowmeter Engineering Handbook's

correlation is the best compromise for x >

95%

for the orifice. They wisely advocated

5.8 EFFECTS OF MORE THAN ONE FLOW COMPONENT

115

1.20

1.05-

1.00

0.04

(a)

0.08 0.12

Moisture content

0.16

O20

1.20

1.15

1.10

ii 1.00

0.95

0.90

0.85

0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00

(b) Oryness fraction, x

Figure 5.12. Wet steam flowmeter correction factor, (a) Proposed expressions

plotted against moisture content y, where x is the dryness fraction (from Owen

and Hussein

1991;

reproduced with permission of Elsevier Science), (b) Com-

parison between data for wet steam correction factor and proposed factors from

the literature (from Hussein and Owen 1991; reproduced with permission of

Elsevier Science).

(1) x"

(2) Separated flow model

(3) Murdock's correlation

(4) James

correlation

(5) 'Shell Flowmeterlng Engineering Handbook*

(6) Homogeneous flow model and x~*

(7) BS 3812:1964

116 ORIFICE PLATE METERS

1.10 -

1.0

0.90 -

Symbol

•

Reynolds number

= 1.5 x 10

= 8 x 10

= 4 x 10

= 1.5 x 10

rv n n

1 1 1

x •

1 1

0.1 0.2 0.3 0.4 0.5

Oil fraction

0.6 0.7

0.8

Figure 5.13. Performance of orifice meter in an oil-in-water emulsion (from Pal

and Rhodes 1985; reproduced with permission of BHR Group).

an upstream separator and indicated that several types of upstream separators give

a value of x > 95% with reasonably low pressure loss. Owen et al. (1991) provided

further convincing experimental evidence for the benefits of fitting a separator in

a steam line before an orifice plate. The separator, of course, should make more

accurate flow measurement possible. They showed that slugs of water in a gas flow,

trapped by valves and then released, can travel at 50 m/s or more and result in impact

pressures at 5 bar tank pressure of, in some cases, well over 50 bar. One of the orifices

they used was made of 3-mm-thick mild steel and had deformed very substantially

after 20 impacts.

Wenran and Yunxian (1995) suggested a simple model for deducing flow rate

and phase fraction for steam flows in orifice plates, and they claim that errors were,

respectively, 9 and 6.5% for their model. The reader is referred to the original article

for more details. Pressure noise has also been suggested as a means of obtaining

more information in steam-water flows (Shuoping et al. 1996). (cf. Fischer's 1995

calculation for gas-liquid annular mist).

Oil-in-Water Flows

Pal and Rhodes (1985) reported results of tests of orifice meters in horizontal oil-

water mixtures. Figure 5.13 shows the effect of increasing oil content on each meter.

Pal (1993) tested orifices with a range of oil-in-water emulsions ranging from 30

to 84% (inversion took place at

78%

oil) and found that stable emulsions introduced

coefficient changes within about 3% using a generalized Reynolds number, which

is defined in the paper, but for unstabilized emulsions the changes were greater.

Other Applications

Murdock (1961) reported correlations to within ±1.5% for two-phase flow. Others

are reported by Lin (1982) and Mattar et al. (1979). Washington (1989) claimed