2003 PROCEEDINGS PAGE 39AMERICAN SCHOOL OF GAS MEASUREMENT TECHNOLOGY

AN OVERVIEW OF THE McCROMETER V-CONE METER AMERICANSCHOOL OF GAS MEASUREMENT TECHNOLOGY 2003

Dr. RJW Peters and Dr. R. StevenMcCrometer

3255 W, Stetson Ave., Hemet, CA 92545-7799

INTRODUCTION

The V-Cone meter is a differential pressure (DP) typemeter patented by McCrometer Inc. a subsidiary ofDanaher Corporation. The V-Cone meter is in manyrespects a classical DP meter using the physical laws ofthe conservation of mass and energy as its principle ofoperation. However, there are important differencesbetween the V-Cone meter design and other DP metertypes. These differences give the V-Cone meter importantperformance advantages. These advantages nclude theability of the V-Cone meter to operate with very shortupstream and downstream straight pipe lengths, tocreate a low total pressure (or “head loss”), to create avery stable DP, to give a large turn down, to createrelatively low signal noise and to cope well with liquidand particulates in the gas stream. The aim of this paperis to discuss the design of the V-Cone meter and explainwhy this design gives these advantages over traditionalDP meters.

1. The V-Cone Meter is a DP Meter

The V-Cone meter like several other popular meters is adifferential pressure (or “DP”) meter. These meters allwork according to the same principle. That is anobstruction in the pipe (i.e., a reduction in the crosssectional area available to the flow) causes an increasein flow velocity and a corresponding reduction inpressure. Hence be measuring the upstream pressure,the temperature and the difference in the static pressurebetween the upstream and the minimum cross sectionalareas the flowrate can be determined as long as the fluidproperties are known. The flow rate determination is doneby applying the laws of conservation of mass and energy.

The difference in the DP meter designs is the particulargeometry of the primary element (in particular theobstruction in the pipe creating the pressure and velocitychange). With the traditional DP meters the obstructionhas consisted of blocking the outside of the flow area invarious ways thus forcing the fluid to accelerate througha reduced opening in the centre of the pipe line. Examplesof this are the Orifice Plate, Venturi and Nozzle metersas shown in Figure 1.

The Orifice Plate is a plate with a hole in the centerinserted between two pipe flanges. The Nozzle is acontoured converging section (or “nozzle’) discharginguncontrolled into the full pipe area and the Venturi(sometimes called “Venturi Tube”) has a converging

FIGURE 1. Traditional DP meters.

section (or “nozzle”), a length of straight pipe of reducedarea comparative to the upstream pipe (or “throat”) anda diverging section (or “diffuser”) to allow a controlleddischarge. Clearly these meters all accelerate the flowtowards the center line of the pipe. The V-Cone meterdoes the opposite. It accelerates the flow to the outsideof the pipe by having a cone positioned pointing up thecenter line of the on coming flow. Figure 2 shows thegeometry of the V-Cone.

FIGURE 2. V-Cone meter sketches.

From Figure 2 it can be seen that the V-Cone meterupstream tapping (denoted “H” to in indicate the highpressure port) is on the wall of the pipe but thedownstream tapping (denoted “L” to in indicate the lowpressure port) is not on the wall of the pipe but on theback face of the cone on the pipe center line. This is aradical departure from the traditional DP meter designsand this design gives some significant performanceimprovements which will be discussed in chapter two.

The different geometry can cause some engineers towonder if the V-Cone meter operates according to adifferent principle than the traditional DP meters but thisis not so. The governing flow equation for the V-Cone isidentical to that of all other DP meters. From the userspoint of view all secondary equipment used is exactlythe same as would be chosen for any DP meter. That isthe same manifolds, DP transmitters and FlowComputers are used as are used with other DP meters

PAGE 40 2003 PROCEEDINGSAMERICAN SCHOOL OF GAS MEASUREMENT TECHNOLOGY

√

√

(with the flow computer requiring the V-Cone equationjust as it requires the unique equation for any DP meter).Therefore use of a V-Cone meter requires no furtherunderstanding than that knowledge required to use anyother DP meter. Figure 3 illustrates the typical set up ofany DP meter.

FIGURE 3. A typical DP meter set up.

Now that it is known that the V-Cone meter is similar inset up and use to all other DP meters the differencescaused by having a cone in the primary element can bediscussed.

2. The Differences (and Advantages) Between V-ConeMeters and Traditional DP Meters

2.1) The Flow Equation

All DP meters work according to the principles of theconservation of mass and energy. This results in equation1.

m = EYCdAd √2ρ∆P (1)

where m is the mass flowrateE is the “Velocity of Approach Factor” √

___

Y is the expansibility factor.Cd is the discharge coefficient (i.e. the ratio of

the actual to theoretically predicted flow-rates).

Ad is the minimum cross sectional area throughthe meter.

ρ is the fluid density.∆P is the measured differential pressure.β is the square root of the ratio of the minimum

flow cross sectional area through the meterto the inlet cross sectional area.

Depending on specific DP meter geometries some ofthe above parameters are calculated in different ways.For the V-Cone the following should be noted.

a) Due to the different geometry the V-Cone meter betaratio is not calculated by the standard equation 2 but byequation 3.

Ad dβTraditional = A D

βV-Cone =Ad dc √

2

A D ↵

where A is the upstream pipe cross sectional area, d idthe traditional throat diameter, D is the upstream pipediameter and dc is the cone diameter. Figure 4 illustratesthe origins of these equations.

FIGURE 4. The Difference in beta calculations betweenthe V-Cone and traditonal DP meters.

b) Clearly the calculation of the minimum cross sectionalarea for the V-Cone meter will be different to thetraditional DP meters. The comparisons are shown inequations 4 & 5.

AdTraditional =π d2 (4)4

AdV-Cone =π (D2 - d

2c) (5)

4

c) The Expansibility (Y) Equation

For all DP meters including the V-Cone meter if the fluidflowing is liquid the expansibility factor is effectively unityas the expansion factor corrects for changes in densitythrough the DP meter and liquids are effectivelyincompressible. If the fluid is a gas however the flow iscompressible and the correction factor is required. The

= (2)

(3)√= 1-

βTraditionaldA

A

d

D= =

βV Coned cA

A

d

D− = = −

1

2

Orifice Plate V-Cone

2003 PROCEEDINGS PAGE 41AMERICAN SCHOOL OF GAS MEASUREMENT TECHNOLOGY

Orifice Plate meter has an experimental expansibilityequation as shown in equation 6. The V-Cone meter hashad its expansibility equation found by experiments atNEL in the UK [1]. The V-Cone meter expansibilityequation is shown in equation 7.

Orifice Plate Meter: (6)

V-Cone Meter: (7)

κ is the isentropic exponent and P1 is the upstreampressure. Again it is clear that the V-Cone meter behavessimilarly to other DP meter devices.

d) The Discharge Coefficient, Cd and MeterCalibration

For all DP meters the discharge coefficient is defined asshown in equation 8.

(8)

Where mactual is the actual flowrate and is the theoreticalflowrate calculated by consideration of the masscontinuity equation and Bernoulli (energy) equation.

V-Cone meters need to be “calibrated” to find the valueof the discharge coefficient. Calibration for all DP metersconsists of using a reference meter of extremely lowuncertainty (which gives a flowrate value as close to theactual flowrate as can practically be managed) upstreamof the DP meter in question and fitting the results toequation 8. Over a large turn down (a wide range offlowrates) V-Cone meters are found to have a dischargecoefficient which is a function of the upstream pipe flowReynolds number. For small turndowns an averageddischarge coefficient is often sufficiently accurate formany applications. Figure 5 shows a typical V-Conemeter calibration.

Note that in Figure 5 the discharge coefficient line fit isquoted to have an uncertainty of 0.5%. This is the quoteduncertainty for all V-Cone meters. To achieve thisMcCrometer calibrates all meters over the operationalrange of the flow.

The latest version of ISO 5167 [2] recommends thatVenturi meters should be calibrated for flows where theReynolds number is greater than one million. Thus, theVenturi and V-Cone meters have similar calibration

requirements. Orifice Plate meters (and Venturi metersat Reynolds numbers lower than one million) do not needto be calibrated as long as the upstream and downstreamflow conditions are met as then the discharge coefficientcan be read off a table [2]. However, these upstreamand downstream straight lengths are considerable andas the V-Cone meter does not need these extra pipelengths (see section 2.2) the weight and space saved bya V-Cone meter can match the extra cost of the pipework or flow conditioner required making the V-Conemeter extremely competitive.

For any given V-Cone meter (or any other DP meter) if aconstant discharge coefficient is used then with a readupstream pressure and differential pressure and with thefluid properties known equation 1 can be directly applied.If any given V-Cone meter (or any other DP meter) has aline fit describing the discharge coefficient to theReynolds number relationship found by calibration thenan iterative solution is required. The Reynolds number iscalculated by equation 9. The iteration for a V-Cone meter(or any other DP meter) is given by equation 10. A startingflowrate for the iteration is recommended to be that foundby initially considering the discharge coefficient to beunity. This ensures a quick convergence of the iteration.

4mRe = (9)πµD

where Re is the flows upstream Reynolds numberm is the mass flowrateD is the upstream pipe diameterµ is the fluid viscosity

4mm - EYAdf 2π∆P = 0 (10)πµD

Y = 1 - (0.41+0.35β4) ∆P κP1

Y = 1 - (0.649+0.696β4) ∆P κP1

mactual mactual

Cd = mtheoretical = EYAd √_____2ρ∆P

FIGURE 5. A typical calibration graph for a V-Cone meter.

√___

√√√↵

√√√↵

m EYA fm

DPd

..

−

=42 0

πµρ∆

PAGE 42 2003 PROCEEDINGSAMERICAN SCHOOL OF GAS MEASUREMENT TECHNOLOGY

4mwhere Cd = f(Re) = f πµD

2.2) Flow Conditioning

An advantage the V-Cone meter has over other metersis that it is a flow conditioner as well as a flow meter.This results in the meter having the ability to operate ininstallations where other meters in the market (DP andnon-DP meters) can not. With space and weight in manyindustrial applications being important the savings inspace, weight and cost of avoiding the requirement forlarge straight lengths of pipe upstream and downstreamof the metering station by using a V-cone meter can beconsiderable.

The V-Cone meter will continue to operate as theupstream length is reduced to less than the minimumallowed by other meter designs. In fact V-Cone metershave been installed successfully directly onto thedownstream flange of various pipe disturbances (e.g. 900

bends, out of plane double bends, valves etc) andcontinued to give reliable readings. Figures 6 and 7 showthe difference in using an Orifice Plate meter and a V-Cone meter in a confined space. The test graphs arecourteously of NIST.

FIGURE 6. An Orifice Plate meters performance atvarious distances downstream of a double out of plane

bend.

Figures 6 and 7 where published in the ASME FluidsEngineering Conference 1993 [3]. Further independentverification of the V-Cone meters ability to continue tooperate in poor installations that have a-symmetricalvelocity profiles and heavy swirl is given by Chevron andStatoil who presented results of swirl tests on the V-Conemeter at the North Sea Flow Measurement Workshop in1995 [4]. Chevron and Statoil concluded “Since the

accuracy of V-Cone meters are not significantly affectedby swirl flow, they are better suited for applications incramped quarters than Orifice Plate meters.”

2.3 A Stable Differential Pressure

With the V-Cone meters unique positioning of thedownstream pressure port on the back face of the conethe differential pressure is very stabile. In fact, with thedownstream port not in direct contact with the flow pastthe minimum cross sectional area, what is in reality beingread is the pressure created by the vortices generatedbehind the cone. The strength of these vortices (andhence the magnitude of the DP read) is dictated by theshear force of the jet coming off the end of the cone.Hence, the vortices strength is a direct indication of theflowrate.

Figure 8 shows a sample result of experimentsconducted to show the relative fluctuation in the DPreadings of a 1/2” Orifice meter and a 1/2” V-Cone meter.The paramerer δ is the standard deviation of the DParound its mean.

Clearly the V-Cone has less pressure fluctuations thanthe Orifice Plate meter. Figure 8 is from an internalMcCrometer report [5].

2.4) The V-Cone Meter Turn Down

The V-Cone meters turndown (i.e., the ratio of highest tolowest readable flow with in the quoted 0.5% uncertainty)is 10:1 for a single DP transmitter. This is considerablyhigher than other DP meters (e.g., an Orifice Plateturndown for a single DP transmitter is typically 3:1). Thisperformance is due to the positioning of the downstreampressure port on the back end of the cone and thestability of the DP signal produced.

√√√↵C f f

m

Dd = ( ) =

Re

.

4

πµ

FIGURE 7. An V-Cone meters performance at variousdistances downstream of a double out of plane bend.

2003 PROCEEDINGS PAGE 43AMERICAN SCHOOL OF GAS MEASUREMENT TECHNOLOGY

FIGURE 8. A comparison of the DP signal fluctuations ofOrifice Plate and V-Cone meters.

Figure 9 is shows a recently calibrated V-Cone meterholding an uncertainty of 0.54% across a turndown of18:1 for a single DP transmitter.

FIGURE 9. A calibrated V-Cone meter showing highturndown.

2.5) The Total Pressure (or “Head”) Loss

The total head loss of the V-Cone meter is relatively lowcompared to other DP meters and many other type of flowmeters. In fact the V-Cone meter head loss is comparableto the Venturi meter (i.e., the DP meter traditionallydesigned to be low head loss meter). Note that both theV-Cone meter and the Orifice Plate meter do not measurethe pressure at a point in contact with the streamlines ofthe main flow but rather at a point in contact with thevortices. (see Figure 10a and Figure10b).

If it is also noted that the typical discharge coefficient ofthe Orifice Plate meter is 0.6 [2] and the typical dischargecoefficient of the V-Cone meter is 0.8 then for a givenflow rate and equivalent meter geometries Equation 1shows that the differential pressure of the V-Cone meteris less than for the Orifice meter. As the upstreampressure is the pipe pressure before it is influenced bythe meter in question then the higher differential pressure

produced by the Orifice Plate indicates a lowerdownstream pressure which indicates stronger vortices.This therefore is the reason why the V-Cone meter has alower total head loss than the Orifice Plate meter asstronger vortices means greater energy losses.

Miller [6] gives the head loss calculations for differentmeters. Figure 11 shows a comparison of many metersthat have had their total head loss predicted according tothe equations given by Miller. Water in a 3” pipe line wasused with a flow rate of 1145 liters per minute flow rate.Clearly the V-Cone meter is similar to the Venturi metersand better than the other meters in this comparison.

2.6 Contaminated Flows

The V-Cone meter is sturdy and copes with particulatesin the flowing fluid well. The cone is protected by theboundary layer that exists around it so most small solid

FIGURE 10a. The Orifice Plate meter pressure portposition relative to the vortices.

FIGURE 10b. The V-Cone meter pressure port positionrelative to the vortices.

PAGE 44 2003 PROCEEDINGSAMERICAN SCHOOL OF GAS MEASUREMENT TECHNOLOGY

particles tend not to strike the cones edge and thereforethe cone survives in abrasive flows longer than manyother meters. It does not wear quickly unlike an OrificePlates sharp edge. When damage does occur tests haveshown that even moderate damage to the cones edgearound the minimum cross sectional flow area has hadonly a small effect on the meters performance. Due tothe geometry of the V-Cone meter there is no place forcontaminates to collect and therefore the meter tendsto be self cleaning.

2.7 Wet Gas Flow Metering

Wet gas metering is becoming increasingly essential inmany different industries. DP meters are considered tobe one of the better single phase meters for use in wetgas flows (i.e., gas flows with a relatively small quantityof liquid present). All DP meters tend to give a positiveerror (called an “over-reading”) when liquid is present ina gas flow. The V-Cone meter allows most of the liquidphase in a wet gas to pass by undisturbed along thepipe wall meaning it tends to have a relatively smallpositive error compared to other DP meters.

Figure 12 shows a comparative plot of the effect of liquidin a gas flow on a geometrically equivalent (0.55 betaratio) V-Cone meter and Venturi meter. The quantity ofliquid is shown in terms of a parameter called theLockhart-Martinelli parameter denoted by “X.” Equation11 defines X.

m1 ρgX = (11)mg ρ1

where mg and m1 are the gas and liquid mass flowratesrespectively.

ρg and ρ1 are the gas and liquid densitiesrespectively.

Thus in Figure 11 with a constant pressure of 60 Bar(i.e., set fluid densities) the parameter X is indicating theratio of liquid to gas mass flowrates in the wet gas. TheV-Cone meter has a slightly smaller liquid induced errorthan the Venturi meter. The spread visible for both metertypes at the higher relative liquid to gas ratios is partiallydue to a relationship between over-reading and pressureamong other effects but this is beyond the scope of thispaper. What is clear however, is that the V-Cone metercontinues to operate when liquid is present in the gasflows and for a given liquid to gas ratio it reads with arepeatable and therefore predictable error.

FIGURE 12. A plot showing the comparativeperformance of a V-Cone meter and aVenturi meter used with wet gas flow.

STANDARDS

The V-Cone meter is covered by the API 5.7 documentfor differential pressure meters [7]. It also has custodytransfer approval in Canada.

CONCLUSIONS

The V-Cone meter is a relatively new meter on the marketthat operates according to the same principles as othertraditional DP meters but with significant advantages.These are the elimination of large pipe runs, a stabledifferential pressure is produced, a high turndown isobtained using a single DP transmitter, a low head lossis produced, the meter is more resistant to wear thanmany other designs and handles wet gas flows betterthan any other DP meter. These advantages are slowlybecoming known through out the many industries andthe V-Cone meters market share is continuing to increasethrough out the world.

REFERENCES

1. Reader-Harris M. et al. North Sea Flow MeasurementWorkshop 2001, “Derivation of an ExpansibilityFactor for the V-Cone Meter.”

FIGURE 11. A plot of Millers total head loss calculations[6] for 3” meters with 1145 liters per minute flow rate.

Xm

m

l

g

g

l

=

.

.

ρρ

2003 PROCEEDINGS PAGE 45AMERICAN SCHOOL OF GAS MEASUREMENT TECHNOLOGY

2. ISO 5167 Rev. 4, “Measurement of Fluid Flow byMeans of Pressure Differential Devices Inserted inCircular Cross-Section Conduits Running Full.”

3. Ifft S. ASME Fluids Engineering Conference 1993,“Pipe Elbow Effects on the V-Cone Flowmeter.”

4. Shen J. et al. North Sea Flow MeasurementWorkshop, 1995 “A Performance Study of a V-ConeMeter in Swirling Flow.”

5. Ifft S. McCrometer Internal Report “Signal NoiseRatio Comparison with V-Cone and Orifice Plate.

6. Miller R. “Flow Measurement EngineeringHandbook” 3rd Ed. Published by McGraw Hill.

7. API 5.7 “Testing Protocol for Differential PressureFlow Measurement Devices.”