Rosemount Manual: Rosemount Annubar® Primary Flow Element Flow Test Data Book Manuals & Guides
Reference Manual
Rosemount 485 Annubar Rosemount 585 Annubar
00821-0100-4809, Rev BA
July 2009
Rosemount Annubar® Primary Flow Element
Flow Test Data Book
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Reference Manual
00821-0100-4809, Rev BA
July 2009
Rosemount Annubar
Flow Test Data Book
Rosemount Annubar Primary
Flow Element Flow Test
Data Book
NOTICE
Read this manual before working with the product. For personal and system safety, and for
optimum product performance, make sure to thoroughly understand the contents before
installing, using, or maintaining this product.
Customer Central
1-800-999-9307 (7:00 a.m. to 7:00 P.M. CST)
National Response Center
1-800-654-7768 (24 hours a day)
Equipment service needs
International
1-(952) 906-8888
The products described in this document are NOT designed for nuclear-qualified
applications.
Using non-nuclear qualified products in applications that require nuclear-qualified hardware
or products may cause inaccurate readings.
For information on Rosemount nuclear-qualified products, contact an Emerson Process
Management Sales Representative.
.
.
Fisher-
Rosemount satisfies all obligations coming from legislation to harmonize product
requirements in the European Union
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Reference Manual
00821-0100-4809, Rev BA
July 2009
Rosemount Annubar
Flow Test Data Book
Table of Contents
SECTION 1
Annubar
Technology
SECTION 2
How the Annubar
Works
SECTION 3
Flow Coefficient
Reynolds Number
Independence
SECTION 4
Annubar Flow
Theory
Rosemount Annubar Primary Flow Element. . . . . . . . . . . . . . . . . . . . . . . . . . . .1-1
Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-1
Mechanical and Structural Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-2
In-House Performance Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-2
Independent Laboratory Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-2
On-Site Performance Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-2
Rosemount Annubar Flow Element Test Advantages. . . . . . . . . . . . . . . . . .1-2
Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-1
Design and Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-2
Rosemount 485 Annubar Sensor Design . . . . . . . . . . . . . . . . . . . . . . . . . . .2-2
Rosemount 585 Annubar Sensor Design . . . . . . . . . . . . . . . . . . . . . . . . . . .2-5
Flow Coefficient Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-1
Benefits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-1
Rosemount Annubar Reynolds Number Ranges . . . . . . . . . . . . . . . . . . . . . . . .3-2
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-1
Flow Equation Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-2
Blockage Equation Derivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-3
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-5
SECTION 5
Test Facilities and
Procedures
SECTION 6
References
Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-1
Testing Laboratories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-1
Rosemount Boulder, Colorado Flow Laboratory . . . . . . . . . . . . . . . . . . . . . .5-1
Alden Research Laboratories (ARL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-1
SwRI Gas Research Institute (GRI), Meter Research Facility (MRF) . . . . . .5 -1
Utah Water Research Laboratories (UWRL). . . . . . . . . . . . . . . . . . . . . . . . .5-1
Colorado Engineering Experimental Sation Inc (CEESI). . . . . . . . . . . . . . . .5-1
Gravimetric Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-2
Testing Performed by Sensor Size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-3
485 Sensor Size 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-4
485 Sensor Size 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-10
485 Sensor Size 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-26
585 Sensor Size 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-28
585 Sensor Size 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-39
585 Sensor Size 44 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-49
TOC-1
Rosemount Annubar
Flow Test Data Book
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July 2009
TOC-2
Reference Manual
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July 2009
Rosemount Annubar
Flow Test Data Book
Section 1 Annubar Technology
Rosemount Annubar Primary Flow Element . . . . . . . . . .page 1-1
Rosemount Annubar Flow Element Test Advantages . . .page 1-2
The Rosemount Annubar primary flow element maintains the traditional
strengths of Averaging Pitot Tubes (APTs) with improved performance. The
strengths of the Rosemount Annubar include:
• Low permanent pressure loss
• A flow coefficient independence of Reynolds number
• Simple installation, including a gear drive insertion and retraction
device
• The highest signal to noise ratio of any APT (Model 485)
• 485 Uncalibrated Accuracy: ±0.75%
• 485 Calibrated Accuracy: up to ±0.5%
• 585 Uncalibrated Accuracy: ±1.50%
• 585 Calibrated Accuracy: up to ±0.5%
• Integral temperature measurement
• Direct transmitter mounting capability
ROSEMOUNT ANNUBAR PRIMARY FLOW ELEMENT
The Rosemount 485 Annubar primary flow element is the fifth generation
Annubar. This design is comprised of three separate tubes that are drawn to
produce a unique geometrical shape that produces a high and low pressure
signal and contains an integral thermowell. The geometry change to the
sensor required testing to establish a characterization curve and to determine
a new flow coefficient.
The Rosemount 585 Annubar primary flow element is machined from a single
piece of barstock in a diamond shape with sharp edges to produce a flow
coefficient that is more linear to Reynold’s number than other designs.
Testing Tests performed on the Annubar primary flow elements are divided into five
major categories:
• Research and development testing
• Mechanical and structural testing
• In-house performance testing
• Independent laboratory testing
• On-site performance testing
All categories are on-going and continue to be a part of the current Emerson
test program for the Annubar primary flow ele m en ts.
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Rosemount Annubar
Flow Test Data Book
Mechanical and
Structural Testing
Material and structural testing at:
Reference Manual
00821-0100-4809, Rev BA
July 2009
Rosemount performed mechanical and structural testing 485 585
Material hardness X
Moments of inertia X X
Fatigue life X X
Fluid loading due to lift and drag forces X
Static bend tests X
Allowable stress limits X X
Failure analysis X X
Vibration analysis X X
• Hauser Laboratories
• MicroMotion Laboratory
• Eden Prairie Flow Laboratory
In-House Performance
Testing
Independent Laboratory
Testing
On-Site Performance
Tests
ROSEMOUNT ANNUBAR FLOW ELEMENT TEST ADVANTAGES
Hundreds of flow tests were perfor med in the Em erson flow laborator y in 2-in.
to 12-in. pipeline, using independently certified magnetic meters as primary
reference meters. Baseline K-values, sign al no ise , cavitation, high and low
Reynolds number limitations, methods of installations, static modeling, and
straight-run requirements are just a few of the in- house performance tests th at
were performed on the Rosemount Annubar primaries.
Rosemount Annubar primary flow element models were tested at four
independent laboratories:
• Alden Research Laboratory (ARL)
• Colorado Engineering Experiment Station, Inc. (CEESI)
• Southwest Research Institute (SwRI)
• Utah Water Research Lab (UWRL)
Certified flow-data sheets were supplied from each of these facilities in
pipelines ranging from 2-in. to 24-in. over a wide range of Reynolds number s.
A representative sample of independent tests conducted at Emerson and
independent laboratories are Section 5: Test Facilities and Procedures.
Emerson Process Management has a field service department that performs
on-site performance tests and in-line calibrations for customers with unique
installations or applications.
Emerson test procedures incorporat e th e follo win g criter ia and adv an tages:
• Flow test data were collected over a flow turndown range of 10:1 in
most cases
• All coefficients are ±0.75% (95% confidence) of the published K-value
of a particular 485 Annubar flow element.
• All coefficients are ±1.50% (95% confidence) of the published K-value
of a particular 585 Annubar flow element.
1-2
Reference Manual
QKDP
Flow
Stagnation Pressure
Stagnation Pressure
Impact
Pressure
P
L
P
L
P
L
P
H
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Rosemount Annubar
Flow Test Data Book
Section 2 How the Annubar Works
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .page 2-1
Design and Performance . . . . . . . . . . . . . . . . . . . . . . . . . . page 2-2
OVERVIEW The Rosemount Annubar primary flow element is a device used to measure
the flow of a liquid, gas or steam fluid that flows through a pipe. It enables flow
measurement by creating a differential pressure (DP) that is proportional to
the square of the velocity of the fluid in the pipe, in accordance with Bernoulli's
theorem. This DP is measured and converted int o a fl ow rate usin g a
secondary device, such as a DP pressure transmitter.
The flow is related to DP through the following relationship.
Equation 2-1
where:
Figure 2-2. Cross Section of the
Rosemount 485 Annubar in a
Flow Stream
Q = Flow Rate
K = Annubar Flow Coefficient
DP = Differential Pressure
For a more complete discussion on the flow equation, refer to Section 4:
Annubar Flow Theory.
The Annubar generates a DP by creating blockage in the pipe and acting as
an obstruction to the fluid. The velocity of the fluid is decreased and stalled as
it reaches the front surface the Annubar sensor, creating the impact/high
pressure.
The Rosemount Annubar senses the impact pressure by utilizing either a
frontal slot (485) or sensing hole (585) design, which opens into the high
pressure chamber. This high pressure chamber connects directly into the DP
transmitter for measurement.
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Rosemount Annubar
DP PHPL–=
Thermowell
Low Pressure Plenum
Low Pressure Plenums
High Pressure
Plenum
Flow Test Data Book
Figure 2-3. Cross Section of the
Rosemount 585 Annubar in a
Flow Stream
As the fluid continues around the Annubar sensor, it creates a lower velocity
profile on the backside of the sensor, creating the low/suction pressure
downstream of the Annubar. Individual ports, located on the backside of the
Annubar sensor measure this low pressure. Working on the same principle as
the high pressure, an average low pressure is maint aine d in th e lo w pr essure
chamber that connects directly into the transmitter for measurement.
Reference Manual
00821-0100-4809, Rev BA
July 2009
DESIGN AND PERFORMANCE
Rosemount 485 Annubar
Sensor Design
Figure 2-5. Cross-Section of the
Rosemount 485 Annubar
The resultant differential pressure is the difference between the impact (high)
pressure reading and the suction (low) pressure reading as seen below.
Equation 2-4
where:
PH = High Pressure
PL = Low Pressure
The 485 Annubar is T-shaped in design and is constructed in three scaled
sizes for use in a wide range of pipe diameters. Its design includes a single
high-pressure plenum, three common low-pressure plenums, and an integral
thermowell.
2-2
Reference Manual
Upstream slot for
accurate averaging
Seal weld between
high pressure and
low pressure
plenums
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Rosemount Annubar
Flow Test Data Book
Differential Pressure (DP) Signal
The T-shaped design of the 485 Annubar generates more differential
pressure than any APT. The flat upstream surface of the sensor is
perpendicular to the direction of flow, which results in a high and very stable
drag coefficient. Since the flow coefficient, or k factor (see Equation 2-1), is a
function of the drag coefficient, this produces a large, repeatable and
predictable DP signal for a given velocity.
The magnitude of the DP signal is directly related to measurement accuracy
and the amount of primary element turndown, particularly at lower flow rates.
One traditional limitation of APT technology is that accuracy degrades at
lower flow rates as a result of the minimal DP produced. The Rosemount 485
extends the lower range limit that an APT can measure and maintain
performance as a result of the additional DP generated.
Impact (High) Pressure Measurement
As mentioned in the “Overview” on page 2-1, the Rosemount 485 Annubar
measures the impact (high) pressure with a frontal slot design. The laser cut
slots extend across the entire front surface of the sensor to maximize the
amount of the velocity flow profile measured and increase the accuracy o f the
measurement. Multiple slots are used to maintain the structura l integrity of the
bar. A seal weld is visible around the perimeter of th e slots and is u sed to seal
the high pressure chamber from the low pressure chamber to prevent any
leakage potential. Testing revealed that the raised surface of the weld does
not have any effect on performance so it is not removed.
Figure 2-6. Rosemount 485
Frontal Slot Design
The patented slot design replaces sensing ports used by traditional APTs.
This slot “integrates” the velocity flow profile and improves the accuracy of the
measurement. By “integrating” the flow profile, a consistent series of data is
recorded across the pipe diameter instead of limited samples taken at a few
discreet points. By increasing the number of samples taken across the pipe of
the actual flow rate, the accuracy of the measurement is improved.
2-3
Rosemount Annubar
Stagnation
Zone
Short Arrows Indicate Low Velocities
Boundary Layer
Separation Point
Long Arrows Indicate High Velocities
Flow Test Data Book
Suction (Low) Pressure Measurement
The Rosemount 485 Annubar measures the suction (low) pressure with
sensing ports located in stagnation zones on the backside of the sensor. As
the fluid comes into contact with the 485 Annubar sensor and separates from
the front edges, the velocity and turbulence level of the fluid in the area
directly behind the sensor is greatly decreased. The low velocity and
turbulence level in this stagnation zone significantly reduces any pressure
variation in this region. Individual sensing ports are drilled in this location to
detect the suction (low) pressure.
The number of ports located on the backside of a given sensor is a fun ction of
pipe size and mathematically determined by the same Cheb yshev principles
of previous Annubar designs.
Figure 2-7. Velocity Graph
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00821-0100-4809, Rev BA
July 2009
2-4
Surface Texture
As the flow over any surface in the flow stream is increased, the character of
the fluid flow near that surface goes through a transition. At a certain critical
flow rate, the level of turbulence in this region, termed the boundary layer,
increases sharply. This increase in turbulence in the boundary layer on the
front surface of the 485 Annubar causes a marked change in the separation of
the flow at the edge, which in turn affects the accuracy of the differential
pressure signal. The transition from the non-turbulent (laminar) to a turbulent
boundary layer condition is an inescapable fact described by the principles of
fluid dynamics. However, it has been found that altering the roughness or
texture of the surface adjacent to the boundary layer can control the flow at
which that transition takes place.
Reference Manual
Low Pressure Plenums
High Pressure
Plenum
00821-0100-4809, Rev BA
July 2009
Rosemount Annubar
Flow Test Data Book
The front surface of the 485 Annubar sensor is tailored to the customer's flow
application. In high flow applications (where the maximum expected flow
exceeds one million Reynolds number), the surface is textured to increase the
level of turbulence at a given flow rate. This ensures that the transition from
laminar to turbulent flow in the boundary layer occurs at flows below (and
outside) the customer's measurement ra nge. For lower flow applications, the
surface is left smooth to maintain a laminar boundary layer forcing the
transition to occur above the maximum flow that will be seen in the
application.
Rosemount 585 Annubar
Sensor Design
Figure 2-8. Cross-Section of the
Rosemount 585 Annubar
The 585 Annubar is diamond-shaped in design and is constructed in three
scaled sizes for use in a wide range of pipe diameters.
Reynolds Number Considerations
As the flow over any surface in the flow stream is increased, the character of
the fluid flow near that surface goes through a transition. At a certain critical
flow rate, the level of turbulence in this region, termed the boundary layer,
increases sharply. This increase in turbulence in the boundary layer on the
front surface of the 585 Annubar causes a marked change in the separation of
the flow at the edge, which in turn affects the accuracy of the differential
pressure signal. The transition from the non-turbulent (laminar) to a turbulent
boundary layer condition is an inescapable fact described by the principles of
fluid dynamics. However, on the 585 model, the sharp edges on the side of
the Annubar produce a more consistent separation point, resultin g in a flow
coefficient that is linear over the entire range of pipe reynolds numbers that
are typically encountered in flow measurement applications.
2-5
Rosemount Annubar
Flow Test Data Book
Reference Manual
00821-0100-4809, Rev BA
July 2009
2-6
Reference Manual
00821-0100-4809, Rev BA
July 2009
Rosemount Annubar
Flow Test Data Book
Section 3 Flow Coefficient Reynolds
Number Independence
Flow Coefficient Overview . . . . . . . . . . . . . . . . . . . . . . . . . page 3-1
Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 3-1
Rosemount Annubar Reynolds Number Ranges . . . . . .page 3-2
FLOW COEFFICIENT OVERVIEW
The flow coefficient (K–factor) is the ratio of the actual flow rate to the
calculated (theoretical) flow rate. The accuracy of the Rosemount Annubar
relates directly to the flow coefficient. The flow coefficient is empirica lly
determined by testing a representative sample of flowmeters to establish the
relationship between flowrate and the DP induced across the primary
element.
This sampling of flow coefficients is generally plotted as a function of key
flow-meter variables. For averaging pitot tubes, flow coefficients are plotted
against the meter's pipe blockage.
Curve-fitting techniques are used to generate an equation that best fits the
sampling of flow coefficients. This curve-fit equation becomes the basis for a
manufacturer's published flow coefficients. These published flow coefficients
are used for flowmeters in nearly all untested conditions.
Rosemount has supplemented the flow coeffi cient equations discussed above
with the blockage equation derived in Section 4 of this document. This
blockage equation defines a relationship between flow coefficient and
blockage that substantiates the results of empi rical testing. Extensive APT
testing conducted by Rosemount over the past 35 years support the
theoretical equation.
BENEFITS The K-factor of an Annubar is a function of the blockage the probe present s to
the flow stream. The flow coefficient of many other primary elements is a
function of Reynolds number. This characteristic of Annubar performance
offers significant benefits over other pr imary elements.
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K-factor independence can be attributed to a constant separation point at the
edges of the Annubar and to the probe's ability to take a proper average.
Thus:
• It allows measurement of a wide range of Reynolds numbers without a
correction factor for changing Reynolds numbers.
• Any variations in the K-factor with changing Reynolds number are due
to scatter and fall within ±0.75% of the published K-value for the 485
Annubar.
• Any variations in the K-factor with changing Reynolds number are due
to scatter and fall within ±1.50% of the published K-value for the 585
Annubar.
Rosemount Annubar
R
d
dV
--------------------- -=
Flow Test Data Book
The K-to-blockage theoretical link demonstrates a higher degree of
confidence in Rosemount Annubar K-factors than shown by flowmeters that
use only an empirical database to determine flow coefficients. Rosemount is
the first company to identify and use theoretical equations linking
self-averaging pitot-tube flow coefficients to pipe blockage.
Reference Manual
00821-0100-4809, Rev BA
July 2009
ROSEMOUNT ANNUBAR REYNOLDS NUMBER RANGES
Table 3-1. Rod Reynolds
Number Lower Limits
For a Rosemount Annubar to operate accurately, the flowing media must
travel at a velocity sufficient to separate from the edges of the Annubar.
Drag coefficients, lif t coeffic ients, sep aration point s, and pressure distributions
around bluff bodies are best de scribed by “rod” Reynolds numbers. There is a
minimum rod Reynolds number at which the flowing fluid will not properly
separate from the edges of the T shape. The rod Reynolds number can be
calculated using Equation 3-1.
Equation 3-1
where:
d = Probe Width (feet or meters)
V = Velocity of fluid (ft/sec or meters/second)
= Density of fluid (lbm/ft
3
or kg/m3)
= Viscosity of fluid (lbm/ft-sec or kg/meter-sec)
Minimum rod Reynolds numbers for the Ro se mou nt Annub ar can be fou nd in
Table 3-1.
Sensor Size Minimum Rod Reynolds Number (Rd) Probe Width (d)
feet meters
485 Annubar
1 6500 0.0492 0.0150
2 12500 0.0883 0.0269
3 25000 0.1613 0.0491
585 Annubar
11 6500 0.0667 0.0203
22 10000 0.1000 0.0305
44 25000 0.1900 0.0579
3-2
Reference Manual
cross-sectional area of sensor
cross-sectional area of pipe
Actual Flow Rate (QA)
Theoretical Flow Rate (Q
th
)
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Rosemount Annubar
Flow Test Data Book
Section 4
Annubar Flow Theory
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 4-1
Flow Equation Derivation . . . . . . . . . . . . . . . . . . . . . . . . . .page 4-2
Blockage Equation Derivation . . . . . . . . . . . . . . . . . . . . . . page 4-3
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 4-5
Annubar flow equations are built on basic hydraulic principles. The theoretical
link to these concepts increases confidence in an Annubar measurement
when compared to other measurement s that are based solely on empirical
data.
NOMENCLATURE The following symbols are used in the derivation of the flow equation and the
blockage equation:
A = cross sectional area of the pipe
B = blockage ratio =
C
= integration constant
1
C
= integration constant
2
f(B) = function of blockage
h
= differential pressure caused by blockage
B
h
= differential pressure caused by shape of sensor
S
h = total differential pressure = h
gc = gravitational constant
K
= flow coefficient =
A
P = fluid pressure
Q
= actual flow rate
a
Q
= theoretical flow rate
th
V = average fluid velocity
= fluid density
z = height above an arbitrary datum plane
Unless noted otherwise, subscript 1 denotes an upstream condition and
subscript 2 denotes a downstream or throat co nditio n.
+ h
B
S
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Rosemount Annubar
V
1
2
2g
c
---------
P
1
1
------ gcz
1
++
V
2
2
2g
c
---------
P
2
2
------ gcz
2
++=
V
2
2g
c
P1P2–
------------------------
=
h
P
1P2
–
-------------------=
V
2
2gch=
QaKAAV=
QaKAA12gch=
Flow Test Data Book
Reference Manual
00821-0100-4809, Rev BA
July 2009
FLOW EQUATION DERIVATION
The flow equation relates the DP induced across a primary element to the
velocity of the fluid in the pipe. As with other differential-pressure flowmeters,
Rosemount Annubar equations are based on the Bernoulli equation:
Equation 4-1
For incompressible fluids
element are negligible so z
= 2. Changes in elevation around a primary
1
= z2.
1
Also, assume the velocity just within the mouth of the impact-sensing ports is
zero, (V
= 0). While minor circulation may occur within the high pressure
1
chamber of the Rosemount Annubar, this flow is extremely small and may be
considered negligible.
Solving for V
yields:
2
Equation 4-2
The net differential pressure produced can be rewritten as:
Equation 4-3
Substituting Equation 4-3 into Equation 4-2 yields:
Equation 4-4
Like the orifice plate and venturi meter, the general equation describing the
actual flow in a pipe for the Rosemount Annubar is:
Equation 4-5
In Equation 4-4, V
is the average velocity of the fluid traveling past the
2
sensor on the downstream side; whereas, in Equation 4-5, V is the average
velocity in the pipe. Differences between these two velocities (V
absorbed in the flow coefficient (K
).
A
and V) are
2
Combining Equation 4-4 and Equation 4-5 yields:
Equation 4-6
Equation 4-6 is the flow equation used to relate differential pressure induced
across the primary element to flow rate for the Rosemount Annubar.
4-2
Reference Manual
KAfB=
h
B
P1P2–
------------------------
1
2g
c
---------
V
2
2
V
1
2
–==
A1V11A2V2
2
=
V
2
A
1
A
2
------
V
1
=
A21B–A
1
=
V
2
1
1B–
------------ -
V
1
=
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Flow Test Data Book
BLOCKAGE EQUATION DERIVATION
Because the flow coefficient compensates for the difference between V2 and
V, it must be recognized that (K
obstructed area the sensor itself causes in the pipe. More specifically, (K
) will be a function of the amount of
A
A
) is
a function of the sensor's blockage in the pipe.
Equation 4-7
This is analogous to the velocity-of-approach factor for an orifice plate or a
venturi meter. The following derivation uniquely determines f(B) in
Equation 4-7. Discussion is limited to fluid flows in the turbulent regime for
which Rosemount Annubar flow measurement is intended. Development of
the equations applies to primary flow elements that are geometrically similar.
Beginning with Equation 4-6, the differential pressure produced by a primary
flow element can be dissected into two parts:
•
Differential pressure due to the primary flow element's blockage (h
•
Differential pressure due to the shape o f the primar y flow element (h
B
Focusing on the differential pressure contribution due to the primary flow
element's blockage (h
Equation 4-8
In the derivation of the blockage equation V
velocity in the pipe prior to encountering the primary flow element, V
), Equation 4-1 can be rearranged:
B
is defined as the average fluid
1
equals
2
the accelerated velocity past the primary flow element.
)
)
S
Using the conservation of mass:
Equation 4-9
For incompressible fluids,
= 2, Equation 4-9 can be simplified:
1
Equation 4-10
Where:
A
= Cross-sectional area of the pipe
1
A
= Cross-sectional area of the pipe less the amount blocked by the sensor
2
A
can be rewritten in terms of A and the flow element's blockage:
2
Equation 4-11
Substituting into Equation 4-10 yields:
Equation 4-12
4-3
Rosemount Annubar
h
B
V
1
2
2g
c
---------
1
1B–
2
-------------------- -
1–=
QaKAA1 2gch=
K
A
Q
A
12gchBhS
+
------------------------------------------------------=
K
A
h
B
----------
1
2
-- -
Q
a
A12g
c
---------------------
h
BhS
+
3
2
-- -–
–=
h
B
B
--------- -
V
1
2
g
c
---------
1B–
3–
=
K
A
h
B
----------
K
A
h
B
--------------
h
B
B
--------------
=
K
A
B
----------
1
2
-- -–
Q
A
A12g
c
---------------------
h
BhS
+
3
2
-- -–
V
1
2
g
c
---------
1B–
3–
=
V
1
Q
A
1
------=
h hBhA+=
K
A
B
----------
Q
a
A12gch
-----------------------------
3
– 1B–
3–
=
K
A
Q
a
A12gch
-----------------------------=
K
A
B
---------- K
A
3
1B–
3–
=
KAd
K
A
3
----------
–
1B–3–Bd
=
1
2
-- -
K
A
2–
C1+
1
2
-- -
1B–
2–
=
Flow Test Data Book
Substituting Equation 4 -12 into Equation 4-8:
Equation 4-13
Recall the general equation relating the actual flow in a pipe to the
Rosemount Annubar signal (Equation 4-6):
Where:
h = The total differential pressure produced by the flow elem e nt
h = h
Substituting into Equation 4-6 and rearranging yields:
Equation 4-14
Differentiate Equation 4-14 with respect to the differential pressure
contribution due to the primary flow element's blockage (h
remains constant.
+ hS
B
Reference Manual
00821-0100-4809, Rev BA
July 2009
), assuming hS
B
Equation 4-15
Differentiate Equation 4-13 with respect to the primary flow element's
blockage (B).
Equation 4-16
Combine with Equation 4-15 and Equation 4-16.
Equation 4-17
Substitute and and simplify:
Equation 4-18
Substitute and simplify:
4-4
Equation 4-19
Rearrange and integrate:
Equation 4-20
Reference Manual
K
A
1B–
1C
1
1B–
2
–
------------------------------------------=
K
A
1C2B–
1C
1
1C2B–
2
–
--------------------------------------------------=
K
A
B0
1
1C
1
–
--------------------=
1
1C
1
–
--------------------
00821-0100-4809, Rev BA
July 2009
Rosemount Annubar
Flow Test Data Book
Where C1 = constant of integration, solve for KA, redefining the integration
constant C
Equation 4-21
(B) represents the actual blockage in the pipe caused by the Rosemount
Annubar. Because downstream pressure is sensed past the flow element's
widest cross-section, the effective blockage of the sensor will be a fraction of
the actual blockage. Therefore, define an ef fective blockage as C
represents a fraction of the actual blockage. Equation 4-21 can be rewritten:
Equation 4-22
Equation 4-22 shows that there is a direct relationship between a primary flow
element flow coefficient K
Equation 4-22 becomes:
Equation 4-23
as 2C1.
1
B where C2
2
and its blockage. As blockage approaches zero,
A
Thus, as blockage approaches zero, the primary flow element flow coefficient
approaches a constant value , the stream-flow coefficient.
This constant value is the primary flow element flow coefficien t due only to the
primary flow element's shape (h
), and is analogous to placing the primary
S
flow element in an infinitely large pipe with no confining walls.
The constants C
and C2 in Equation 4-22 are determined experimentally.
1
Once determined, Equation 4-22 becomes the theoretical link between the
flow coefficient and the flow element blockage.
CONCLUSION While empirical testing of a flowmeter is the most accurate means of
determining the meter's flow coefficient, many flowmeters use untested
predicted flow coefficient.
•
Untested flow coefficients are based on a representative sample of
empirically determined flow coefficients and on theories that link the
flow coefficient to physical parameters in the pipe.
•
Like an orifice plate or a venturi meter, an averaging pitot tube has a
theoretical relationship between its flow coefficient and parameters in
the pipe.
•
An averaging pitot tube's flow coefficient is related to it s blockage in the
pipe. This blockage dependency is necessary because the sensor it self
reduces the effective pipe flow area.
•
For an orifice plate and a venturi meter, the velocity-of-approach factor
is the theoretical link between the meter's flow coefficient and it's beta
ratio. For a Rosemount Annubar, Equation 4-22 describes the
theoretical relationship between the sen so r's flow coe fficient and its
blockage in the pipe.
•
Using a theoretical basis, in addition to empirical testing, for the
prediction of untested flow coefficients provides a much higher degree
of confidence in these untested values.
4-5
Rosemount Annubar
Flow Test Data Book
Reference Manual
00821-0100-4809, Rev BA
July 2009
4-6
Reference Manual
00821-0100-4809, Rev BA
July 2009
Rosemount Annubar
Flow Test Data Book
Section 5 Test Facilities and Procedures
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .page 5-1
Testing Laboratories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 5-1
Gravimetric Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . .page 5-2
Testing Performed by Sensor Size . . . . . . . . . . . . . . . . . .page 5-3
485 Sensor Size 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .page 5-4
485 Sensor Size 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .page 5-10
485 Sensor Size 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .page 5-26
585 Sensor Size 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .page 5-28
585 Sensor Size 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 5-39
585 Sensor Size 44 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 5-49
OVERVIEW The following descriptions of tests and testing methods are abbreviated
versions. For detailed descriptions of the individual laboratories contact the
facility in question.
TESTING LABORATORIES
Rosemount Boulder,
Colorado Flow
Laboratory
Alden Research
Laboratories (ARL)
SwRI Gas Research
Institute (GRI), Meter
Research Facility (MRF)
Utah Water Research
Laboratories (UWRL)
Colorado Engineering
Experimental Sation Inc
(CEESI)
The Rosemount Annubars are tested and calibrated in water at Rosemount
Inc. Line sizes available for testing range from 0.50 in. to 12 in. A secondary
set of reference meters, routinely calibrated against a gravimetric primary
standard, provide an uncertainty of 0.25 percent. Calibrations that use the
primary-measurement device, gravimetric method, can be calibrated with an
uncertainty of 0.1 percent.
Flowmeters are calibrated at ARL using the gravimetric method. This method
has been found to produce a consistent accuracy of ±0.25% over extended
periods.
Flowmeters are tested and calibrated on a recirculating natural gas loop. A
sonic nozzle bank provides secondary flow calibration. This permits high
repeatability and excellent test accuracies via calibration against the
gravimetric primary standards. The sonic nozzle banks produce an accuracy
on flow rate of 0.25% of reading.
Flowmeters are calibrated at UWRL using either calibrated nozzles or
gravimetric method.
CEESI has two facilities, using different calibration methods:
• The Nunn, Colorado Facility uses compressed air stored in cylinders
and discharged through a calibrated nozzle.
• The Garner IA Facility uses high-pressure natural gas from a
transmission line that is measured via a calibrated nozzle.
www.rosemount.com
Rosemount Annubar
Flow Test Data Book
Reference Manual
00821-0100-4809, Rev BA
July 2009
GRAVIMETRIC PROCEDURE
Piping is selected to match the inside diameter of th e flowmeter under test.
Carbon steel piping is normally used for these tests. Gaskets between pipe
flanges are carefully installed and checked to ensure that they not interfere
with the flow. Proper alignment of the flowmeter with the piping is maintained.
After all piping is secured with bolts, couplings, or clamps. Water is gradually
introduced into the line. Flows are set to purge air from the system and to
bring the flowmeter to steady-state temperature. After operating the system
for a period of time, the control valve (at the downstream end of the test line)
is closed. Air is then purged from all instrumentation lines, instruments, and
the flowmeter.
After air purging, and with the control valve in the closed position, all
instrumentation is checked for zero-flow indication. Calibration test runs are
not started until all instrumentation reads zero at the no flow condition.
The flow rate is set by adjusting the control valve at the end of the test line to
a desired flow. This flow is allowed to stabilize and reach steady-state
condition. This condition is achieved when the average flow-meter readout is
constant with time. At this point, the calibration run begins.
A calibration run consists of simultaneously recording the flowmeter output
while the weighing tank is filled and the filling process is timed. Electronic
timers are activated and deactivated by elec tr ic eye s on the switch way.
Outputs are recorded at 1–15 Hz during this time. The duration of the run is
typically between 50 and 100 seconds. For higher flow rates, the limiting
factor is the capacity of the weighing tank.
In addition to recording weight and time, the water temperature, air
temperature weigh tank, and air temperature adjacent to the readout are
recorded. Barometric pressure is also recorded at the start and at the end of
the test.
After a run is completed, the control valve is reset to another flow rate and the
process is repeated. Runs are normally conducted at 12 different flow rates,
approximately equally spaced from the maximum to the minimum flow rates.
In some cases, the maximum flow obtainable by the test facility determines
the upper flow limit of the test.
5-2
Reference Manual
00821-0100-4809, Rev BA
July 2009
Rosemount Annubar
Flow Test Data Book
TESTING PERFORMED BY SENSOR SIZE
The followings tests are provided on the following pages
Rosemount 485 Sensor Size 1:
• Water, FI-210, 3-in. Schedule 40 (see page 5-4)
• Natural Gas, FI-260, 3-in. Schedule 40 (see page 5-6)
• Natural Gas, FI-261, 3-in. Schedule 40 (see page 5-8)
Rosemount 485 Sensor Size 2:
• Natural Gas and Water, FI-156, 8-in. Schedule 80 (see page 5-10)
• Water, FI-162, 3-in. Schedule 40 (see page 5-12)
• Water, FI-163, 3-in. Schedule 40 (see page 5-14)
• Water, FI-169, 10-in. Schedule 40 (see page 5-16)
• Natural Gas and Water, FI-178, 8-in. Schedule 80 (see page 5-18)
• Natural Gas and Water, FI-179, 8-in. Schedule 80 (see page 5-20)
• Natural Gas, FI-180, 6-in. Schedule 40 (see page 5-22)
• Natural Gas, FI-181, 6-in. Schedule 40 (see page 5-24)
Rosemount 485 Sensor Size 3
• Water, FI-307, 24-in. Schedule Standard (see page 5-26)
Rosemount 585 Sensor Size 11:
• Water, 585-11-1, 4-in. Schedule 40 (page 5-29)
• Water, 585-11-1, 4-in. Schedule 40 (page 5-31)
• Water, 585-11-7, 10-in. Schedule 40 (page 5-33)
• Water, 585-11-6, 8-in. Schedule 40 (page 5-34)
• Water, 585-11-5, 6-in. Schedule 40 (page 5-35)
• Water, 585-11-5, 6-in. Schedule 40 (page 5-36)
• Water, 585-11-3, 4-in. Schedule 80 (page 5-37)
• Air, 585-11-1, 4-in. Schedule 40 (page 5-38)
Rosemount 585 Sensor Size 22:
• Water, 585-22-1, 6-in. Schedule 80 (page 5-40)
• Water, 585-22-1, 6-in. Schedule 80 (page 5-42)
• Water, 585-22-5, 10-in. Schedule 40 (page 5-43)
• Water, 585-22-5, 10-in. Schedule 40 (page 5-44)
• Water, 585-22-5, 10-in. Schedule 40 (page 5-45)
• Water, 585-22-2, 5-in. Schedule 40 (page 5-46)
• Water, 585-22-2, 5-in. Schedule 40 (page 5-47)
• Air, 585-22-5, 8-in. Schedule 10 (page 5-48)
Rosemount 585 Sensor Size 33
• Water, 585-44-1, 16-in. STD (page 5-50)
• Water, 585-44-1, 24-in. STD (page 5-51)
• Water, 585-44-1, 12-in. STD (page 5-52)
• Natural Gas, 585-44-10, 12-in. STD (page 5-53)
5-3
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