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

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7.6 DESIGN CONSIDERATIONS

147

where b

represents the contribution of methane, and a

f represents the contribu-

tion of other components. The square root of the compressibility factor is given

/z^ = a

(7.14)

, b

, a

, and b

are tabulated against temperature and pressure, and f is obtained

from

f = X(C

) + 2X(C

) + 3X(C

) - \

X(CO

)

(7.15)

Limits are set to the mole fraction X of each component, and the value of f is zero

for methane. The uncertainty resulting from this formula is estimated for methane

at 70 bar as ±0.25% and for a maximum value (f = 0.2) as ±0.45%.

Weberg (1990) has developed a new critical mass flow correlation for 0-180 bar

and 280-340

This was based on critical mass flow rates computed from the AGA-8

(1992) equation and from Aly and Lee's (1981) ideal gas specific heat correlation.

Average deviation of the correlation from the data was 0.2% (cf. Starling 1994 on

hydrocarbon mixture equations of state).

7.6 DESIGN CONSIDERATIONS

Referring to Figures 7.3 and 7.7, some details are given from the standard (cf. ISO

9300 for full details). Wall smoothness, curvature, and axial distances from inlet

plane are denned. The inlet plane is that plane perpendicular to the axis, which cuts

the inlet toroid at a diameter of 2.5d.

Swirl and other upstream disturbances (cf. Yoo et al. 1993) may need to be elimi-

nated with a straightener. Drain holes to remove condensation may also be necessary

to avoid an accumulation of water reducing the upstream plenum.

These points are summarized here.

Region I

• Average roughness <15 x 10~

• Free from deposits of any sort

• Radius of toroid (in plane through the

axis) 1.8d< r < 2.2d

• Contour toroidal to <0.001d

Region D

• Diffuser half-angle between 2.5° and 6°

• Length of diffuser from toroid at least d

• No discontinuities exceeding 1% of lo-

cal diameter

• Average roughness <10~

Inlet Plane

• Denned by 2.5d ±0.Id intercept

>2.5d

* flush burr free

<0.1 c/

radius

< 0.08 D

preferably

< 12 mm

Figure 7.7. Details of pressure tap.

148 CRITICAL FLOW VENTURI NOZZLE

Swirl free

• Inlet flow to be swirl free, if necessary, by use of a straightener at >5D

p Ratio

• either fi = d/D to be less than 0.25 for a circular inlet pipe or there must be a

large space with >5d in all directions from the axis.

Drain Holes

• <0.06D at greater than one diameter upstream of po tapping and away from the

plane of tapping

The design of the pressure tappings is shown in Figure 7.7 where

the diameter

of the tapping. The inlet tapping should be situated 0.9-1.ID upstream of the inlet

plane, or in a large inlet chamber it should be within lOd ± Id from the inlet plane.

The downstream pressure tapping (if required) should be less than 0.5 times the

conduit diameter from the nozzle exit plane. In some cases, downstream pressure

will be known (e.g., when the nozzle exhausts to the atmosphere).

The inlet temperature tapping should be positioned to give a reliable measure of

stagnation temperature.

The accuracy of the method will depend heavily on the accuracy of measurement

pQ.

Takamoto et al. (1993a) showed that cross flows can cause errors due to the

lack of a measure of stagnation. If we cannot assume that the flow is negligible in

the upstream pipe, then

cannot be directly measured at the wall tapping, and we

shall have to deduce it from pi using

where Mi will be small, but the additional step is likely to reduce the precision of

the final measurement. Similar considerations apply to T

. It is, therefore, preferable

to ensure that stagnation conditions do exist in the inlet plenum.

Pereira et al. (1993) suggested making the nozzle throat and diffuser in two parts

with an O-ring between and discussed the effect of

step between throat and diffuser,

which they found was not critical within certain limits.

7.7 MEASUREMENT UNCERTAINTY

The equation for the uncertainty summation [cf. Equation (5.26) for alternative

equivalent symbols] is

€(q

) = ±[t(A*)

+ 6(C)

+ e(C*)

e(p

)

+ ^(M)

^(T

)

]

1/2

(7.17)

If we apply some of the possible uncertainties mentioned earlier, we have

€(C) = ±0.5% based on the values for the ISO equation

e(CJ = ±0.45% as given for a value for / = 0.2 (but may be too

optimistic)

7.8 EXAMPLE 149

€(A) = ±0.8%

€{%)

for a 5-mm diameter throat would require

0.010-mm uncertainty in throat diameter

guess ±0.5%

guess ±0.1%

guess ±0.2%

With these values, we obtain an overall uncertainty of

€

) = ±1.18%

Caron (1995) gave some details of the critical nozzle test stand designed and used

by the Ford Company to calibrate air-flow sensors. The ASME Standard toroidal

design was selected, and it was reckoned that after calibration an uncertainty of

±0.25%

in the coefficient could be achieved. The paper gives the following values

for uncertainties (the area is calibrated out):

Source

Pressure

Temperature

Discharge coefficient

Critical flow function

Combined uncertainty

Uncertainty

±0.05%

±0.37%

±0.25%

±0.0125%

Sensitivity

Coefficient

0.5

Product

±0.05%

±0.185%

±0.25%

±0.0125%

±0.315%

Because this omits, due to calibration, the measurement of the throat area

and uses higher precision values, it is not out of line with the value obtained

earlier.

7.8 EXAMPLE

Using the data given in this chapter, we shall calculate the mass flow of air q

for a

throat diameter d of

mm, inlet stagnation pressure p

of 2 bar, and inlet stagnation

temperature T

of 50°C, and we shall calculate the outlet area necessary to allow

operation with a back pressure p2 up to 1.6 bar.

In this example, we are assuming a venturi nozzle conforming to the preceding

requirements. We need to calculate the value of Re

, and for this we require the

throat velocity. At critical conditions, M = 1, and the velocity is that of sound speed

(cf. Baker 1996)

(7.18)

Because at M = 1 using Equation (2.15),

To y + 1

2y RT

+ l M

150 CRITICAL FLOW VENTURI NOZZLE

and because T

= 323.15

and for air 7 = 1.4 and R/M = 8.3143/29.0 kJ/kgK =

0.2867 kJ/kgK

;

we obtain c

328.8 m/s.

Taking v = 1.3 x 10~

;

we can obtain the Reynolds number for the throat

= 328.8 x 0.006/1.3 x 10"

= 1.52 x 10

(within ISO limits)

Note from Figure 7.6 that small variations of Re

should have little effect on the

value of the discharge coefficient.

Using Table 7.1

C = 0.9935-1.525 Re/

= 0.9896

Using Table 7.2 at T

= 50°C and p

= 2 bar,

C* = 0.6853 (cf. 0.685 using the perfect

gas

value)

From Equation 7.4,

/R/MTo

= Ttd

/4 = 2.827 x 1O"

= 0.01260 kg/s

To obtain the outlet area, we first obtain the value of the outlet Mach number

from Equation (2.45) for ideal flow through the nozzle

Y/iX-Y)

"" V 2

-x

= 0.574

Then from Equation (2.18),

l/2 y-1

^ = 1.22 A

= 3.45 x 1(T

= 6.63 mm

This outlet area has assumed a curve like c in Figure 2.6(b). We have ignored what

happens between curves c and d. In fact, the flow ceases to be without loss. If the

pressure at outlet lies between c and d, the flow will follow d out of the throat before

7.9 INDUSTRIAL AND OTHER EXPERIENCE 151

passing through a sudden pressure increase known as a shock

wave.

Downstream of

this sudden change, the flow will follow a curve below, but not dissimilar to, c.

For our purposes, therefore, it will be advisable to ensure that the outlet diameter

is larger than 6.63 mm (as in Figure 7.4) so that the throat is definitely running at

sonic velocity. ISO 9300 recommends designing for an outlet pressure recovery 80%

of the ideal [Equation

(7.8)].

7.9 INDUSTRIAL AND OTHER EXPERIENCE

The use of the nozzle in saturated steam with a dryness fraction down to 84% re-

quires a wet steam correction factor (Amini and Owen 1995, cf. ASME/ANSIMFC-7M

1987).

However, Amini and Owen suggest that a more practical approach might be

to precede the nozzle with a steam-water separator, assume the steam to be dry satu-

rated, and accept an uncertainty in the mass flow of

3%.

An uncertainty of 1% arises

from the lack of perfect separation.

The Gas & Fuel Corporation of Victoria, Australia, has a gas meter test facility

with 11 critical nozzles (Wright 1993), has been in use for 10 years and has a range of

6-5,600 m

/h for meters from 80 to 450 mm, and another facility with six nozzles,

which has been in use for 5 years and has a range of 2.4-30 m

/h. The coefficient

has ±0.5% uncertainty. The flow rate sequence is that the flow rate of each nozzle is

close to the sum of flows through the next three smaller nozzles. This is achieved by

using a flow rate ratio for each nozzle compared to the one below of 1.839:1. Wright

claimed that the use of two nozzles to match the higher flow rate requires more

nozzles to cover the range. Wright also mentioned a Wheatstone bridge technique

to calibrate nozzles, and an American quantity called standard time, 4 used by the

American Meter Company and equal to the time in seconds to pass one cubic foot

at an inlet pressure of 24.696 psia (10 psig) and an inlet temperature of 60.0°F.

Nakao et al. (1996) described a calibration system for sonic nozzles that used

the weight of a collecting vessel to obtain the flow rate. Four lines were available

for the venturi nozzles, and the gas was drawn through with a vacuum pump until

the required flow conditions were established. The flow line was then changed to

the vessel, which had been evacuated and weighed, and the flow continued until a

sufficient mass had been collected, when the diversion time ended. Care was needed

to allow for dead volumes and the change-over mechanisms. They claimed an overall

uncertainty for the rig of about

±0.1%.

Bosio et al. (1990) observed a lack of repeatability during gravimetric primary

calibration of nozzles in natural gas containing approximately

mg/m

of hydrogen

sulfide. They identified the problem as deposition of sulfur in the throat. Chesnoy

(1993) also discussed the problem of sulfur deposition in the nozzle throat, causing

change in nozzle performance. To reduce the possibility of sulfur formation either

the content of H

S needs to be reduced or the oxidant needs to be eliminated.

If this is not possible, work supported by Chevron suggested that the position of

the deposition moved downstream due to temperature increase (Mottram and Ting

1992).

Chesnoy claimed that K-Lab's primary calibration was within

±0.3%

between

20 and 100 bar.

zinc oxide bed had been used to treat the inlet gas successfully up

to 100 bar (absolute), but other actions were under consideration above this pressure.

152 CRITICAL FLOW VENTURI NOZZLE

Bignell (1996a) described comparison techniques for the performance of a num-

ber of small sonic nozzles, and Kim and O'Neal (1995) used critical flow models to

estimate two-phase flow of HCFC22 and HFC134a through short tube orifices.

Nozzles with throat diameters of 10-1,000 /xm have been reported (Takamoto

1996).

Recent calculations of discharge coefficient using finite elements (Wu and

Yan 1996) gave very impressive agreement with ISO.

7.10 ADVANTAGES, DISADVANTAGES, AND APPLICATIONS

The advantages of this device are that it allows mass flow measurement of gas and

ensures that, provided the flow is choked and, therefore, operating in its correct

regime, flows upstream are not affected by changes in downstream conditions.

It is, however, very inflexible in that flow rate can be increased only by changing

the upstream stagnation values or by increasing the throat area. This leads to the

requirement for a bank of carefully sized nozzles to span the working range.

Its primary application is in gas flow measurement of high precision, particularly

in flow calibration.

7.11 CHAPTER CONCLUSIONS

The critical flow venturi nozzle appears to have the potential for very high preci-

sion. It has been suggested that the ISO uncertainty figure is too great (cf. Gregor

et al. 1993).

It is a meter where upstream conditions should be capable of control and precise

replication so that the profile and turbulence distribution approaching the meter is

always the same.

There are clearly sources of reduced accuracy (e.g., deposits) and possible humid-

ity or small quantities of contaminants in the flow.

It also should be amenable to CFD modeling with increasing precision. The pre-

cise positioning, design, and consequent effect of pressure and temperature tappings

may be amenable to such modeling. Such an approach may suggest, where possible,

a most repeatable and most stable overall layout for the upstream pipe, conditioners,

etc.

Another direction in which experimental and theoretical studies could go is in

the miniaturization of nozzles.

CHAPTER

Other Momentum-Sensing Meters

8.1 INTRODUCTION

The previous chapters have been mainly concerned with devices, the designs of

which have been denned by various standard specifications. In this chapter, we con-

sider other mainly proprietary meters, which depend on the changing flow pattern

and which essentially sense momentum of the flow. The output is in some cases

given by a differential pressure measurement and in others by a position or force

measurement. This means that the user must be aware of the possible effect of den-

sity on the results. Viscosity will also affect some readings.

The somewhat arbitrary order of consideration and the uneven amount of detail

in this chapter reflect the current importance of the devices, the available literature,

and my experience. Thus the variable area meter takes up a large proportion of the

chapter.

The meters to be considered in this chapter are

• variable area (VA) meters, which depend on gravity to oppose the movement of

the float and consist of two main types:

• those with a tapered tube and a float with a fixed metering edge and

• those with an orifice with a fixed metering edge and a moving tapered

Plug;

• spring-loaded profiled plug in an orifice;

• target (drag plate) meter sometimes spring loaded;

• venturi-type meters claiming a low loss, such as Dall, Epiflo, Gentile and Low-

Loss;

• wedge, V-cone meters;

• meters using a bypass with an oscillating vane, a Pelton, or a

meter in it;

• slotted orifice meter;

• pipework features used as meters such as inlets and bends;

• averaging pitots under various names (Annubar, Torbar, etc.); and

• laminar (viscous) flowmeters.

8.2 VARIABLE AREA METER

The variable area (VA) meter is sometimes known as a Rotameter, but this is a trade

name of a particular company and I shall, therefore, refer to it as the variable area

153

154

OTHER MOMENTUM-SENSING METERS

Outlet fitting

O-ring

Float stop outlet

Float

Scale

Tube

Housing

Float stop inlet

O-ring

Inlet fitting

Figure

8.1.

Variable area flowmeter (reproduced with

permission of Bailey-Fischer and Porter).

meter. In the following sections on the VA

meter, I have avoided history, theory, or

other items, which have been consigned

to Appendix 8.A. The reader may also find

practical value in the very useful treatment

by Hogrefe et al. (1995). One way to view

the VA meter is as a variable orifice meter

with a fixed pressure drop resulting from

the weight of the float.

8.2.1 OPERATING PRINCIPLE AND

BACKGROUND

The VA meter consists of a float that rises

up a conical tube due to the upward flow

(Figure 8.1). Float is a misleading term be-

cause it rises not from any buoyant effect

but as a result of the upward drag of the

fluid, which, in turn, results in a pressure

difference across the float. As the flow in-

creases, the float rises higher in the tube to

a point where the annulus formed between

the float and the conical tube wall is sufficient to allow the drag on the float to

balance the float's weight. The flow is then deduced from the height to which the

float has risen. (In Germany, the term swimmer is used rather than float, which may

be more appropriate, but I shall stick with float in this book.)

8.2.2 DESIGN VARIATIONS

Coleman (1956) provided useful information on the development of the float and

tube.

However, we will concentrate mainly on the current practice. Figure 8.2 shows

some of the shapes of floats and of a tube.

Tubes

Tubes are often made of borosilicate glass. In addition to the plain taper tubes, there

are tubes with three longitudinal beads molded into the glass (beaded or fluted

glass) to guide the tail of the float (rib-guided). For very low flow rates a conical

tube with a plumb-bob float or a tri-flat tube with a spherical float is used. For

plain tapered tubes, a central guide is often used (rod-guided). If the fluid or the

operating conditions are unsuitable for glass, a metal tube is used with a fixed orifice

and tapered plug or a tapered tube and disk-head float. Figure

8.2(a)

shows the cross-

section of

tube with guide

beads.

In manufacture, the induction-heated glass tube is

vacuum drawn onto a metal mandrel so designed that several tubes are made at once

in-line.

Floats

There are differing views as to whether centrally guided floats with possible fric-

tion effects offer more repeatable results than unguided floats [Figure 8.2(b)]. An

8.2 VARIABLE AREA METER

155

(b)

Figure 8.2. Tubes and floats: (a) Cross-section of

a tube with guide beads; (b) Float with guide rod;

ity immune float; 3, viscosity nonimmune float; 4,

float for low pressure losses; 5, rotating float) (re-

produced with permission of Bailey-Fischer and

Porter).

Reading edge

alternative is for a tail-guided float, where a ring is held by webs so that the ring

moves on the tube beads and keeps the float central in the tube. Figure

8.2(c)

shows

some float shapes. The development history included attempts to find a viscosity-

independent design. This is most nearly achieved with a sharp edge at the maximum

diameter. The five floats in the figure are a ball float, sharp edged float to reduce vis-

cosity dependence, a viscosity nonimmune float, a float shaped for low pressure loss,

and a rotating unguided float.

8.2.3 REMOTE READOUT METHODS

The most common remote readout method used is magnetic sensing with a metal

tube.

A diagram of a typical mechanism is shown in Figure 8.3. However, designs

using newer field-sensing methods are being introduced.

ISA RP16.4 (1960) deals with extension devices that translate the float motion

into a useful secondary function for indicating, alarming, transmitting, etc. An ex-

tension tube may be used, and magnetic or electrical sensing coils appear to have

been most commonly used.

Liu et al. (1995) described a sensing method for variable area flowmeters that

used the capacitance between two conducting strips on the inner surface of the

tapered tube and the float of good electrical conducting material. The capacitance

156

OTHER MOMENTUM-SENSING METERS

Figure 8.3. Diagram

sensing

for

metal tubes.

between

the

strips will vary

as the

float

rises

in the

tube. They claimed that anal-

ysis

and

experiment have shown that this

sensor system can be used

for

nonconduct-

ing fluids. However, tests reported were

for

a prototype

in a

laboratory

rig and

wider

testing would appear necessary.

Parker (1990) described an optical trans-

ducer.

this,

array

nine infrared

LEDs was mounted

one side

the flow

tube,

and

corresponding array

photo-

transistors was mounted

on the

other

but

displaced

half

the

LED pitch. The read-

ing

each detector,

pair

detectors,

is taken

for

each LED,

and the

responses

are normalized. When

float

present,

the transmission will vary,

and

position-

finding algorithm

claimed

give

reso-

lution

1 part

2048.

8.2.4 DESIGN FEATURES

ISA RP16.1.2.3 (1959) gives

the

recom-

mended main dimensions

of the

connec-

tions

for

the meters,

and

some

these

are

shown

Figure

8.4 for

the glass tube type,

and

sample

the

dimensions

are

given

in Table 8.1.

ISA RP16.1.2.3 (1959) gives

uniform

terminology,

small part

which

has

been reproduced

Figure

8.5. It

also

gives some guidance

precision

and on

safe working pressures

borosilicate glass

tubes.

The manufacturer's instructions

where

read

the

float level should

be ob-

tained (ISA RP16.5 1961a).

other information

available,

the

following may

the

case:

B- -B

-A

Figure

8.4.

Connection dimensions

for

glass tube

type variable area meters (after ISA RP16.1.2.3 1959).

Table 8.1. Sample

dimensions

for

glass tube type VA

meters (after ISA)

Pipe Size

§" (12.7 mm)

(25.4 mm)

(51

mm)

(102 mm)

16§"

(420 mm)

17 §" (445 mm)

21"

(533 mm)

28"

(711 mm)

§"-4" (89-102 mm)

4"-4§"

(102-114 mm)

5"-5§"

(127-140 mm)

6"-7" (152-178 mm)