VIBRATING TUBE DENSIMETER

DENSIMETRE A TUBE VIBRANT

English Abstract

A Coriolis effect densimeter which produces density output data of improved accuracy by embodying the principal that the natural
frequency of a vibrating tube filled with material decreases with an increase in the material mass flow rate. High accuracy output data is
achieved by measuring the natural frequency of the tube as material flows therethrough, correcting the measured frequency to compensate
for the decrease in natural frequency caused the material flow (mass flow rate) and using the corrected natural frequency in the material
density computation.

French Abstract

Un densimètre à effet Coriolis produit des données densimétriques de sortie améliorées grâce à l'application du principe que la fréquence naturelle d'un tube vibrant rempli de matière décroît avec l'augmentation du débit-masse de la matière. Des données de sortie d'une haute précision sont obtenues par la mesure de la fréquence naturelle du tube pendant que la matière s'écoule à travers ce dernier, en corrigeant la fréquence mesurée pour compenser la diminution de la fréquence naturelle causée par l'écoulement de la matière (débit-masse) et en utilisant la fréquence naturelle corrigée dans le calcul de la densité de la matière.

Claims

-26-
WE CLAIM:
1. A method of operating a Coriolis effect meter (10) for
determining the density of material flowing through said meter, said
meter having at least one vibrating tube (130) whose natural frequency
decreases as the mass flow rate of material through said tube
increases, said method comprising the steps of:
measuring the natural frequency of said vibrating tube
(408) as said material flows therethrough;
CHARACTERIZED IN THAT said method further comprises
the steps of:
generating a signal indicative of a corrected frequency
of said tube (522) in response to said measurement of said natural
frequency, wherein said corrected frequency is greater than said
natural frequency by the amount by which said natural frequency is
decreased from said corrected frequency by said material mass flow
rate through said tube; and
generating an output signal specifying the density of said
material flowing through said tube (524) in response to the generation
of said signal indicative of said corrected frequency.
2. The method of claim 1 wherein said natural frequency
is decreased from a zero mass flow rate natural frequency of said tube
in proportion to said material mass flow rate through said tube.
3. The method of claim 2 wherein said method further
comprises the step of measuring the mass flow rate of said material
through said tube (414); and wherein said step of generating said
signal indicative of said corrected frequency comprises the step of
generating said signal indicative of said corrected frequency in
response to said measurement of said mass flow rate.

-27-
4. The method of claim 3 wherein said method further
comprises the step of measuring the volume flow rate of said material
through said tube (417); and wherein said step of generating said
signal indicative of said corrected frequency further comprises the step
of generating said signal indicative of said corrected frequency in
response to said measurement of said volume flow rate.
5. The method of claim 4 wherein said output signal
specifying said density is applied as a feedback signal (418) to generate
said volume flow rate measurement.
6. The method of claim 1 wherein said step of generating
said signal indicative of said corrected frequency includes the steps of:
determining a differential tube period corresponding to
a differential tube natural frequency equal to the amount by which
said natural frequency is reduced in magnitude from said corrected
frequency by said mass flow rate of material in said tube (419); and
combining said differential tube period and a tube
period corresponding to said natural frequency to obtain a corrected
tube period corresponding to said corrected frequency (522).
7. The method of claim 6 wherein said step of determining
a differential tube period comprises the steps of:
multiplying said tube period corresponding to said
natural frequency by the expression (MR x VR x K) where
MR is said mass flow rate of said material,
where VR is said volume flow rate of said material, and
where K is a constant of said meter (419).
8. The method of claim 6 wherein said step of determining
said differential tube period comprises the steps of:

-28-
measuring said mass flow rate MR of said material
(414);
measuring the volume flow rate VR of said material
(417);
specifying a constant K of said meter and
multiplying said tube period corresponding to said
natural frequency by the expression (MR x VR x K) (419).
9. The method of claim 1 wherein said method further
comprises the steps of:
measuring the mass flow rate MR of said material (414);
measuring the volume flow rate VR of said material
(417);
supplying a signal representing a constant K of said
meter;
specifying the expression (1-(MR x VR x K)); and
multiplying a tube period corresponding to said natural
frequency of said tube by said expression to obtain a corrected tube
period corresponding to said corrected frequency (522).
10. The method of claim 1 wherein said method further
comprises the step of:
in response to said measurement of said natural
frequency, generating a tube period corresponding to the natural
frequency of said tube at a zero mass flow rate of said material by
multiplying a tube period corresponding to said natural frequency by
the expression (1-(MR x VR x K));
where MR is the mass flow rate of said material;
where VR is the volume flow rate of said material, and
where K is a constant of said meter (522).

-29-
11. The method of claim 1 wherein said method further
comprises the steps of:
generating a second signal representing a tube period
corresponding to a differential natural frequency of said tube as said
material flows therethrough, said second signal representing a
correction factor specifying the amount by which said natural
frequency of said tube decreases with an increase in the mass flow rate
of said material through said tube (419); and
generating a third signal representing a corrected tube
period corresponding to a zero material mass flow rate natural
frequency of said tube by combining the tube period corresponding to
said natural frequency and said tube period indicated by said second
signal corresponding to said differential frequency (522).
12. The method of claim 11 wherein said density of said
material is determined by solving the expression (524)
Dm= <IMG>
where
Dm = density of said material,
d = Dw - Da,
Dw = density of water,
Da = density of air,
tcm = temp coefficient of tube for measured frequency,
Tc = tube period corrected,
K1 = (tca)Ta2,
Ta = tube period for air--no flow,
tca = temp coefficient of tube for air calibration,
K2 = (tcw)Tw2 - tca(Ta)2,
tcw = temp coefficient of tube for water calibration, and

-30-
Tw = tube period for water--no flow.
13. The method of claim 11 wherein said step of generating
said second signal representing said tube period corresponding to said
differential natural frequency comprises the steps of:
measuring the mass flow rate MR of said material (414);
measuring the volume flow rate VR of said material
(417);
specifying a constant K of said meter; and
multiplying said tube period corresponding to said
natural frequency by the factor (MR x VR x K) (419).
14. The method of claim 11 wherein said step of generating
said second signal representing said differential tube period comprises
the steps of:
multiplying said tube period corresponding to said
natural frequency by the expression (MR x VR x K) (419) where
MR is said mass flow rate of said material;
where VR is said volume flow rate of said material, and
where K is a constant of said meter.
15. The method of claim 11 wherein said method further
comprises the steps of:
measuring the mass flow rate of said material (414);
measuring the volume flow rate of said material (417);
supplying a signal representing a constant K of said
meter;
specifying the expression (1-(MR x VR x K)) where MR
is said mass flow rate and where VR is said volume flow rate and
where K is a constant of said meter (522); and

-31-
multiplying said tube period corresponding to said
natural frequency by said expression to obtain said corrected tube
period corresponding to said zero material mass flow rate natural
frequency (522).
16. The method of claim 1 wherein said method further
comprises the steps of:
in response to said measurement of said natural
frequency, generating a natural frequency correction factor to offset
said natural frequency by the amount by which said measured
frequency is reduced by said mass flow rate (419), and
generating a signal indicative of a corrected frequency
of said tube in response to said generation of said correction factor
(522).
17. The method of claim 16 wherein said step of generating
said signal indicative of a said corrected frequency includes the steps
of:
determining a tube period corresponding to a differential
frequency equal to the amount by which said natural frequency is
reduced in magnitude from a zero mass flow rate natural frequency by
said mass flow rate of said material in said tube (419), and
combining said tube period corresponding to said
differential natural frequency and a tube period corresponding to said
natural frequency to obtain a tube period corresponding to said
corrected frequency (522).
18. The method of claim 1 wherein said step of generating
a signal indicative of a corrected frequency comprises the steps of:
measuring said mass flow rate MR of said material
(414);

-32-
measuring the volume flow rate VR of said material
(417);
specifying a constant K of said meter and
generating said corrected frequency according to the
following equation (419, 522):
.omega.n= <IMG>
.omega.n = said corrected freq.
.omega.? = said measured natural frequency
MR = said mass rate of said material
VR = said volume flow rate of said material
K = said calibration constant of said system
19. An apparatus for ascertaining the density of material
flowing through a Coriolis effect meter (10) having at least one
vibrating tube (130) whose natural frequency decreases as the mass
flow rate of material through said tube increases, said apparatus
comprising:
apparatus for measuring the natural frequency of said
vibrating tube as said material flows therethrough (170, 23);
CHARACTERIZED IN THAT said apparatus further
comprises:
apparatus for generating a signal indicative of a
corrected frequency of said vibrating tube in response to said
measurement of said natural frequency wherein said corrected
frequency is greater than said natural frequency by the amount by
which said natural frequency is decreased from said corrected
frequency by the material mass flow rate through said tube (23, 601,
602, 606); and
apparatus for generating an output signal specifying the
density of said material flowing through said tube in response to said

-33-
generation of said signal indicative of said corrected frequency (23,
608).
20. The apparatus of claim 19 wherein said natural
frequency is decreased from a zero mass flow rate natural frequency
by said material mass flow rate of said tube.
21. The apparatus of claim 20 wherein said apparatus
further comprises means for measuring the mass flow rate of material
through said tube; and wherein apparatus for generating said signal
indicative of said corrected frequency comprises apparatus for
generating said signal indicative of said corrected frequency in
response to said measurement of said mass flow rate (23, 601, 602,
606).
22. The apparatus of claim 21 wherein said apparatus
further comprises apparatus for measuring the volume flow rate of
material through said tube, and wherein said apparatus for generating
said signal indicative of said corrected frequency further comprises
apparatus for generating said signal indicative of said corrected
frequency in response to said measurement of said volume flow rate
(23, 601, 602, 606).
23. The apparatus of claim 22 wherein said signal specifying
said density is applied as a feedback signal to said means for
measuring said volume flow rate to generate said volume flow rate of
said material (23).
24. The apparatus of claim 19 wherein said apparatus for
generating said signal indicative of said corrected frequency includes:

-34-
apparatus for generating a signal representing a
differential tube period corresponding to a differential natural
frequency of said tube equal to the amount by which said natural
frequency is reduced in magnitude by said mass flow rate of material
in said tube (23, 601, 602, 606); and
apparatus for combining said differential tube period and
a tube period corresponding to said natural frequency to obtain a
corrected tube period corresponding to said corrected frequency (23,
601, 602, 606).
25. The apparatus of claim 24 wherein said apparatus for
generating said signal representing said differential tube period
comprises:
apparatus for multiplying said tube period corresponding
to said natural frequency by the expression (MR x VR x K) (23, 601,
602, 606) where
MR is said mass flow rate of said material,
where VR is said volume flow rate of said material, and
where K is a constant of said meter.
26. The apparatus of claim 24 wherein said apparatus for
generating said differential tube period comprises:
apparatus for measuring the mass flow rate MR of said
material (23, 601);
apparatus for measuring the volume flow rate VR of
said material (23, 601);
apparatus for specifying a constant K of said meter; and
apparatus for multiplying said tube period corresponding
to said natural frequency by the expression (MR x VR x K) (23, 606).

-35-
27. The apparatus of claim 24 wherein said apparatus
further comprises:
apparatus for measuring the mass flow rate MR of said
material (23, 601);
apparatus for measuring the volume flow rate VR of
said material (23, 601);
apparatus for supplying a signal representing constant K
of said meter;
apparatus for generating the expression (1-(MR x VR x
K)) (23, 606); and
apparatus for multiplying said tube period corresponding
to said natural frequency by said expression to obtain said corrected
tube period corresponding to said corrected frequency (23, 606).
28. The apparatus of claim 19 wherein said apparatus
further comprises:
apparatus responsive to said measurement of said
natural frequency for generating a signal representing a tube period
corresponding to the natural frequency of said tube at a zero mass
flow rate of said material by multiplying said tube period
corresponding to said natural frequency by the expression
(1-(MR x VR x K)) where MR is the mass flow rate of said material,
where VR is the volume flow rate of said material, and where K is a
constant of said meter (23, 601, 602, 606).
29. The apparatus of claim 19 wherein said apparatus
further comprises:
apparatus for generating a second signal representing a
differential tube period corresponding to a differential natural
frequency of said tube as said material flows therethrough, said second
signal representing a correction factor specifying the amount by which

-36-
said natural frequency of said tube decreases with an increase in the
mass flow rate of said material through said tube (23, 601, 606); and
apparatus for generating a corrected tube period
corresponding to a zero material mass flow rate natural frequency of
said tube by combining a tube period corresponding to said natural
frequency indicated by said first signal and said differential tube
period corresponding to said differential frequency indicated by said
second signal (23, 601, 606).
30. The apparatus of claim 29 wherein said density of said
material is generated by solving the expression (23, 601, 602, 606, 608)
Dm= <IMG>
where
Dm = the density of said material,
d = Dw - Da,
Dw = density of water,
Da = density of air,
tcm = temp coefficient of tube for measured frequency,
Tc = tube period corrected,
K1 = (tca)Ta2,
Ta = tube period for air--no flow,
tca = temp coefficient of tube for air calibration,
K2 = (tcw)Tw2 - tca(Ta)2,
tcw = temp coefficient of tube for water calibration, and
Tw = tube period for water--no flow.

Description

wo 94/2l9g9 ~15 9 O g O PCT/US93/02763
VIBRATING TUBE DENSIM13TE~R
E;lELD OF THE INVENTION
This invention relates to a vibrating tube flowmeter and, more
particularly, to a Coriolis mass flowmeter having density output data
5 of increased accuracy and an increased range of operation.
PROBLl~ - B~(~KGROUND OF THE INVENTION
Prior Coriolis effect ~encimeters~ such as that ~iicrlosetl in the
U.S. Patent 4,876,879 to Ruesch of October 31, 1989, were decigned
and operated with the ~.. plion that the acruracy of the density
me~cllrement is not affected by changes in the mass flow rate,
temperature, viscosity or pressure of the me~c~lred fluid. In particular,
these dencimeters were decigned with the ~c~---..plion that changes in
the natural frequency of the driven flow tubes are only caused by
changes in the density of the m~teri~l flowing through the flow tube.
15 The density me~cllrement wa determined by these meters directly
from the me~cllred natural frequency.
Each Coriolis effect dencimeter hac. a specified set of
recommended operating parameters such as temperature, mass flow
rate, density, viscosity, ~es~ulc~ etc. Coriolis effect meters ~iesigned
20 in accordance with these ~c!~..."l lion have operated s~ticf~rtorily and
given excellent results for most users when their recommended

WO 94/21999 ~ ~, PCT/US93/02763
~5~9~ -2-
operating ranges are not eyt~ee~le~l These meters then norm~lly yield
eYcellent ~r-~ 1'01 ~-ce coupled with a high precision of output data.
However, ci~ es occur in which a Coriolis effect
n~im~ter may be operated beyond its recomm~n~ed operating range
S or near the upper limits of the recommended operating range of flow
rates. Under these con(lition~, the accuracy of the output data is
decreased somewhat as co~ ared to the accuracy of the output data
usually obtained when the meters are operated within their
recc~mmentle~l operating ranges.
Heretofore, when a user required higher mass flow rates, she
or he was required to switch to a higher capacity Coriolis meter in
order to operate the flowmeter with an acceptable pressure drop.
However, advances in the design of Coriolis mass flowmeters have
resnlte-l in lower ~le~ e drops which have effectively broadened the
useful range of the flowmeter. Users operating their flowmeters over
this ~Yt~n-led range, which may exceed the previously recommentled
range, may obtain output data that is not of the highest possible
accuracy.

21~9090
SOLU~ION TO THE PROBLEM
The above problem is solved and an advance in the art is
achieved by the present invention which perrnits output data of high
accuracy to be obtained from Coriolis effect densimeters operating
under conditions in which their heretofore recommended mass flow
rate operating range is exceeded.
It is known by researchers irl this field that the natural
frequency of a vibrating tube of Coriolis effect densimeter is not a
constant, but instead, decreases with increases in the mass flow rate
of material through the vibrating tube. Even though this effect has
been known, it has been disregarded by the designers of the
heretofore available Coriolis effect densimeters. Possible adverse
consequences of this effect were avoided by limiting the operation of
each meter to the lower portion of its theoretical masa flow rate
operating range, because of pressure drop concerns, wherein the effect
is of negligible consequences on the accuracy of the meter output data.
~owever, uses beyond the recommended operating range of early
Coriolis meters resulted in density output data that is less accurate
than the data obtained when the recommended operating ranges are
followed. The reason for this is that when the recommended mass
flow rate operating range is exceeded, the flowmeter is operating at a
point where the decrease in natural frequency is significant. This
decrease in natural frequency becomes even more significant at very
high flow rates.
The problem of obtaining accurate densi~ measurements at
higher ilow rates is solved by the present invention by the provision of
a method and apparatus which takes into account the fact that the
measured natural frequency of a driven flow tube is affected by the
density of the material flowing through the flow tube as well as the
mass flow rate of the material. The measured natural frequency is
corrected by the present invention in accordance with these factors to

wo 94m9g9 PCT/US93/02763
21590~0
obtain a more accurate natural frequency determin~tion- Irhis
corrected natural frequen~y is then used to me~ re the density of the
m~teri~l with high accuracy.

wo Q4,2~ 5 9 ~ 9 ~ PCT/US93/02763
SUMMARY OF T~ INVENTION
The heretofore available C'.orioli.c mass flowmeters were
de-cigne~l and operated as described by the Ruesch patent. Experience
has shown that the Ruesch-type meter works well for a limited range
S of mass flow rates and tlencitiçs. However, it does not take into
account certain char~cterictic~ of a ~ibrating structure that can affect
the meter's accuracy when an attempt is made to expand the operating
range.
A theoretical model that does con.cider other effects of material
flow through a vibrating tube was developed by G. W. Housner in
studies of the Trans-Arabia pipeline in the 1950s. This model is
~liccn~.ced in "Bending Vibrations of a Pipe Line COllt~ llg Flowing
Fluid" by G.W. Housner, JOURNAL OF APPLIED MECHANICS,
Trans. ASME, vol. 74, 1952, pp 205-208. This model is set forth in
an equation derived by Housner which is a one ~limencional fluid
elastic equation describing the undamped, lla~vel~e, free vibration of
a flow tube cont~ining flowing material as follows:
EI ~x4 + ( p fAf+p 6A6) ,~t2 +2p fAfVo aXat + p fAfVo ~X2 -
where
E = modulus of elasticity of the flow tube
I = moment of inertia of the flow tube
pf = density of the m~tçri~l
p ~ = density of the flow tube
Af = cross-sectional area of the flow region
Al; = cross-sectional area of the flow tube
25 vO = flow speed
u(x,t) = transverse displacement of the flow tube
A~proxi,ll~te solutions to Housner's equation for some special
cases reveals the following causal relationship between the natural

wo 94mggg ~ PCT/US93/02763
2~
-6-
frequency of a flow tube and the mass flow rate of fluid flowing
through the tube:
~ ) [ p ~ + p ~ ] {l-Vo( Q )--~1+ 1~ ]~
where
n = integer
~ = tube length
i5I
~, _ p fAf
p ~A~
High precision nnmeric~l c~ tions and detailed tests on actual
Coriolis flowmeters have subst~n~i~te~l the functional relationship
between natural frequency and mass flow rate given by this equation.
This effect m~nifests itself as a decrease in the natural
frequency of the material filled flow tube as the mass flow rate
increases. The only practic~l applic~tion of Housner's equations was
directed toward establishing a critical flow velocity wherein the flow
tube would experience "bllckling" or other instabilities as the natural
frequency decreased to zero. The mass flow rates associated with
15 these phenomena are extremely high compared to those encountered
in commercial flow metering. There has been no known application
of this effect in Coriolis effect meters until the present invention.
The present invention increases the useful operating range of
Coriolis effect densimeters by embcdying the principal that the natural
20 frequency of a driven flow tube decreases as the mass flow rate

wo s4n~ 1 5 9 0 9 0 PCT/US93/02763
increases. The density me~cllrements of prior densimeters ~c~nmed
that the natural frequency of a material filled flow tube was affected
only by ch~n~es in the density of the material flowing through the flow
tube. H<,wGver, accordillg to the method and a~araLus of the present
5 invention, density m~cllrements are determined not only by the
density of the m~teri~l flowing through the flow tube but also are
dependent upon the mass flow rate. The present invention thereby
more accurately me~llres the density of the m~tçri~l at higher
m~teri~l mass flow rates.
The method and apparatus of the present invention determines
the amount by which the natural frequency of a driven flow tube is
decreased because of increases in the m~tcri~l mass flow rate of the
tube. This frequency change inform~tion is used to generate a
corrected value of the natural frequency that is equal to the natural
15 frequency at a zero flow state of the tube. Based on the a~rnx;",~te
solution to Housneis equation presçn~e~l above and experimen~l
collG~ ation. the change in the frequency of osrill~tiQn of the
flowmeter due to the changes in the mass flow rate is set forth below:

WO g4t21999 PCT/US93/02763
( 1-MR VR Kp )
where
~ = the corrected natural frequency of the material filled flow
tube which is the c~ teA no flow natural frequency;
~ = the me~cllred natural frequency of the material filled flow
5 tube;
MR = the mP.~.cllred mass flow rate of the m~teri~l
VR = the me~cllred volume flow rate of the material
densi ty
Kp = a density coeffl~ent CQ~
~ --~
This equation can also be stated in terms of the period of the natural
10 frequency.
Tc = Tm(l-MRVRKp)
Tc = the period collespoi~ding to the corrected natural
frequency
Tm = the period corresponding to the me~cllred natural
15 frequency
The density coefficient constant is developed by calibraffng each
flowmeter using two different subst~n~es, such as air at zero flow,
water at zero flow, and water at flow.

WO 94/21999 ~ ~ ~ 9 ~ ~ ~ PCT/US93/02763
The corrected natural frequency of the material filled flow tube
iS COllvt;l led to a tube period that is then used to calculate the density
of the m~ten~l by solving the following equation:
D (d) ((tcm)T2-Kl) D
where
d = Dw - Da
Dw = density of water
Da = density of air
tcm = temp coefficient of tube for measured frequency
Tc = tube period corrected
10 Kl = (tca)T,2
T2, = tube period for air--no flow
tca = temp coefficient of tube for air calibration
K2 = (tCw)Tw2 - tca(T,)2
tcw = temp coefficient of tube for water calibration
Tw = tube period for water--no flow
In accordance with the present invention, the output of sensor
apparatus connected to or associated with a vibrating flow tube (or
tubes) is connçcted to signal processing circuitry which generates data
indicating the me~c~lred natural frequency of the vibrating flow tube
with material flow, the mass flow rate of the flowing mnaterial, as well
as the volume flow rate of the flowing material. The signal processing
~ ;uilly takes into account the fact that the m~cnred natural
frequency does not remain conct~nt with changes in the mass flow
rate, but decreases with increased mass flow rates. In so doing, the
signal processing ~ ;ui~ly corrects the mç~c~lred frequency and
produces an output speci~ying a corrected natural frequency
corresponding to the zero mass flow rate natural frequency of the
vibrating flow tube. This corrected natural frequency is applied to

WO 94/21999
PCT/US93/02763
a ~ ~
-1~
signal proc:essing c~ y which derives an accurate density in~lic~tiQn
of the material flowing through the flow tube.

WO 94/21999 ~ PCT/US93/1)~70
BRIEF DESCRI:E~IION OF THE DRAW~G
These and other advantages and features of the invention may
be better understood from a reading of the following description
thereof taken in conj~mction with the d~awi~ in which:
Figure 1 discloses one possible exemplary embodiment of the
invention;
Figure 2 ~ ose~ further details of the meter electronics 20 of
Figure 1;
Figure 3 is a curve illuslldli,lg the decreasing natural
frequency/mass flow rate relationship of a Coriolis meter;
Figures 4 and 5 are a flow chart describing the operation of the
meter electronics 20 and its microprocessor 236 as it corrects the
me~cllred natural frequency and c~l~ll~tes density and other
illrol,, ,~1 ;on in accordance with the present invention; and
Figure 6 com~lises a simplified portrayal of Figure 2.

~ 21590~10
DETAILED DESCRIPIION OF
A POSSIBLE PREFERRED EMBODIMENT
One possible preferred exemplary embodiment is illustrated in
Figures 1 through 6. It is to be expressly understood that the present
- 5 invention is not to be limited to this exemplary embodiment. Other
embodiments and modifications are considered to be within the scope
of the claimed inventive concept. The present invention can be
practiced with other types of meters than the described meter.
Successful implementation of the present invention is not dependent
on any meter geometry. Also, other linear approxim~tions for
providing the corrected natural frequency can be utilized.
Figure 1 shows a Coriolis densimeter 5 comprising a Coriolis
meter assembly 10 and meter electronics 20. Meter assembly 10
responds to mass flow rate of a process material. Meter electronics
20 is connected to meter assembly 10 via leads 100 to provide density,
mass flow rate, volume Elow rate and totalized mass flow irlformation
to path 26.
Meter assembly 10 includes a pair of manifolds 110 and 110',
tubular members 150 and 151', a pair of parallel flow tubes 130 and
130', drive mech~nism 180, temperature sensor 190, and a pair of
velocity sensors 17OL and 17OR. Flow tubes 130 and 130' have two
essentially straight inlet legs 131 and 131' and outlet legs 134 and 134'
which converge towards each other at manifold elements 120 and 120'.
The flow tube bends at two symmetrical locations along its length and
are separated by an essentially straight top middle portion. Brace
bars 140 and 140' serve to define the axis W and W' about which each
flow tube oscill~tes.
The side legs 131 and 134 of flow tubes 130 and 130' are fixedly
attached to flow tube mounting blocks 120 and 120' and these blocl~s,
in turn, are fixedly attached to elements 150 and 150'. This provides
a continuous closed material path through Coriolis meter assembly 10.
AME~lDED SHEET

~ WO 94/21999 PCT/US93/02763
9~9Q
-13-
When meter 10 having flange 103 having holes 102 is
connected, via inlet end 104' and outlet end 101' into a flow tube
- system (not shown) which carries the process material that is being
me~mred, material enters the meter through an orifice 101 in flange
103 of end 104 of inlet manifold 110 and is condllcted through a
passageway therein having a gradually ch~nging cross-section to fiow
tube mounting block 120 having a sllrf~ce 121. There, the material is
divided and routed through low tubes 130 and 130'. Upon exiting
flow tubes 130 and 130', the process material is recombined in a single
stream within flow tube mounting block 120' having a surfac~ 121 and
is thereafter routed to exit m~nifold 110'. Within exit manifold 110',
the m~te.ri~l flows through a passageway having a similar gradually
rll~nging cross-section to that of inlet manifold 110 to an orifice 101'
in outlet end 104'. Exit end 104' is connected by fiange 103' having
bolt holes 102' to the flow tube system (not shown).
Flow tubes 130 and 130' are selected and ap~r~liately
mounted to the flow tube mounting blocks 120 so as to have
subst~nti~lly the same mass distribution, moments of inertia and
elastic modulus about bending axes W-W and W'-W', respectively.
These bending axes are located near respective flow tube flanges 140
and 140' and mounting blocks 120 and 120'. The flow tubes extend
outwardly from the mounting blocks in an es.centi~lly parallel f~shion
and have subst~nti~lly equal mass distributions, momentc of inertia
and elastic modulus about their respective bending axes. Tn~cmnch as
the elastic modulus of the flow tubes changes with temperature,
resis~ive tempe,aLule detector (RTD) 190 (typically a pl~tinnm RTD
device) is mounted to flow tube 130', to continllously measure the
tempel~Lure of the flow tube. The temperature of the flow tube and
hence the voltage appearing across the RTD for a given ~-ullent
passing therethrough is governed by the temperature of the material
passing through the flow tube. The temperature dependent voltage

WO 94/21999 2,'~ 9 ~3 g~ PCT/US93/02763
-14-
appearing across the RTD is used in a well known method by meter
electronics 20 to compensate the value of the spring c~ for any
changes in flow tube temperature. The RTD is connected to meter
electronics 20 by lead 195.
Both flow tubes 130 are driven by driver 180 in opposite
directions about their respective bending axes W and W' and at what
is termed the first out of phase natural frequency of the flowmeter.
Both flow tubes 130 and 130' v.brate as the tines of a tuning fork.
This drive mech~ni~m 180 may co~ ise any one of many well known
arrangements, such as a magnet mounted to flow tube 130' and an
opposing coil mounted to flow tube 130 and through which an
alternating ~ elll is passed for vibrating both flow tubes. A suitable
drive signal is applied by meter electronics 20, via lead 185, to drive
mech~ni~m 180.
During oscillation of the flow tubes 130 by drive element 180,
the ~ cent side legs 131, which are forced closer together than their
counterpart side legs 134, reach the end point of their travel where
their velocity crosses zero before their counterparts do. The time
interval (also referred to herein as the phase difference at a particular
frequency, or time difference or simply "1~ t" value) which elapses from
the instant one pair of adjacent side legs reaches their end point of
travel to the instant the cou~terpart pair of side legs, i.e. those forced
further apart, reach their respective end point, is substantially
proportional to the mass flow rate of the material flowing through
meter assembly 10.
To me~cllre the time interval, ~t, sensors 17OL and 17OR are
~tt~rlled to flow tubes 130 and 130' near their free ends. The sensors
may be of any well-known type. The signals generated by sensors 17OL
and 17OR provide a velocity profile of the complete travel of the flow
tubes and can be processed by an,~ one of a number of well known

~159090
methods to compute the time interval and, in turn, the mass flow of
the material passing through the meter.
Sensors 170L and 17OR produce the left and right velocity
signals that appear on leads 165L and 165R, respectively. Using a time
S difference measurement provides an accurate way to measure a
manifestatiorl of the phase difference that occurs between the left and
right velocity sensor signals.
Meter electronics 20 receives the RlL~ temperature signal on
lead 195, and the left and right velocity signals appearing on leads
165L and 165R, respectively. Meter electronics 20 produces the drive
signal appearing on lead 185 to drive element 180 and vibrate tubes
130 and 130'. Meter electronics 20 processes the left and right
velocity signals and the RTD signal to compute the mass flow rate,
volume flow rate and the density of the material passing through
meter assembly 10. This information is applied by meter electronics
20 over path 26 to lltili7~tion means 29. In determining the density,
electronics 20 corrects the measured natural frequency of tubes 130
and 130' in the manner taught by the present invention and then uses
this corrected frequency in its density computation
A block diagraIn of meter electronics 20 is shown in Figure 2
as comprising flow measurement circuit 23, flow tube drive circuit 27
and processing circuitry 235. F1OW tube drive circuit 27 provides a
repetitive alternating or pulsed drive signal via lead 185 to drive
mech~ni~m 180. Drive circuit 27 synchronizes the drive signal to the
left velocity signal on lead 165L and m~int~ins both flow tubes 130 in
opposing sinusoidal vibratory motion at their fundamental natural
frequency. This frequency is governed by a number of factors,
including characteristics of the tubes and the density and mass flow
rate of the material flowing therethrough. Since circuit 27 is known
in the art and its specific implementation does not form any part of
the present invention, it is not discussed herein in further detail. The
AhiEN~lED SI ~EE r

11~ WO 94/21999 21 59 ~ PCT1US93/02763
-16-
reader is illusLldtively referred to United States p~tçnts 5,009,109
(issued to P. Kalotay et al. on April 23, 1991); 4,934,196 (issued to P.
Rom~no on June 19, 1990) and 4,876,879 (issued to J. Ruesch on
October 31, 1989) for a further description of diL~erenl embo-limen
5 for the flow tube drive circuit.
Flow me~cnrement circuit 23 inf ln~ling processing cL.;uilly 235
which processes the left and right velocity signals on leads 165L
and 165R, respectively, along with the RTD signal on lead 195, in a
well known manner, to calculate the m~ss flow rate and volume flow
10 rate of the m~tçri~l p~ssing through meter assembly 10. Output
inform~tion is applied over path 26 to lltili7~tion means 29 which may
be either a display or a process control system. Processing cil~;ui
235 also operates in accordance with the present invention to me~nre
the natural frequency of tubes 130, to correct this frequency, and to
15 use this corrected frequency in deriving highly accurate density
inform~tioIl
Tn~cmn~h as the method by which flow me~cnrement circuit 23
generates mass flow rate and volume flow rate is well known to those
skilled in the art, only that portion of electronics 20 that is germane
20 to the present invention is discussed below. Measurement circuit 23
conLaills two separate input rh~nn~ left channel 202 and right
cll~nnel 212. Each c~nnel cont~in~ an integrator and two zero
crossing detectors. Within both channels, the left and right velocity
signals are applied to respective integrators 206 and 216, each of
25 which effectively forms a low pass filter. The ou~ Ls of these
integrators are applied to zero crossing detectors (effectively
co~ ,a~ators) 208 and 218, which generates level change signals
whenever the corresponding integrated velocity signal exceeds a
voltage window defined by a small predefined positive and negative
30 voltage level, e.g. +2.5V. The oul~uL~ of both zero crossing
detectors 208 and 218 are fed as control signals to counter ~20 to

~WO94121999 ~ 909a PCT/US93/02763
me~cllre a timing interval, in terms of clock pulse counts, that occurs
between colle~onding changes in these outputs. This interval is the
t value and varies with the mass flow rate of the process material.
This l~t value, in counts, is applied in parallel as input data to
processing cil~;uilly 235.
Temperature element RTD 190 is connected by path 195 to an
input of RTD input circuit 224 which supplies a CO~ drive ~;Ullel~l
to the RTD element 190, linearizes the voltage that appears across the
RTD element and col,vel ~ this voltage using vol~age/frequency (V/F)
converter 226 into a stream of pulses that has a scaled requency
which varies proportionally with any changes in RTD voltage. The
resulting pulse stream produced by circuit 224 is applied as an input
to counter 228 which periodically counts the stream and produces a
signal, in counts, that is proportional to the mç~cllred temperature.
The oul~u~ of counter 228 is applied as input data to processing
circuit 235. Procescing circuit 235, which is advantageously a
microprocessor based system, determines the mass flow rate from the
(ligiti7e~ t and temperature values applied thereto. The ~ligiti7ed
temperature value is used to modify a meter factor value based upon
the temperature of the flow tubes. This compçn.c~tes for changes in
flow tube elasticity with tempeLalure. The meter factor, as modified,
(i.e. a temperature compensated meter factor--RF) is then used to
c~ tG the mass flow rate and volume flow rate from the measured
/~ t value arld c~ ted density value. Ha~ing determined the mass
ilow rate and volume flow rate, cir~;uilly 235 then updates output
signals over leads 26 to lltili7ation me~ns 29.
Procescin~ cil~;uilly 235 on Figure 2 in~ln~les microprocessor
236 and memory elements in~llltling a ROM memory 237 and a RAM
memory 238. The ROM 237 stores perm~nent i.lrollllation that is
used by microprocessor 236 in pel~lll~illg its f~lnçtion.c while RAM
memory 238 stores temporary information used by microprocessor 236.

WO 94/21999 2 ~5 ~ ~ 9 PCT/US93/02763
-18-
The microprocessor together with its ROM and RAM memories and
bus system 239 control the overall funetion~ of the proces~ing ~;h~;uilly
235 so that it can receive the signals from counters 220 and 228 and
process them in the manner required to apply, over path 26 to
lltili7~tion means 29, the various iterns of data the Coriolis effect
~len~imeter of the present invention generates.
Some of this i~Ol ~ ;on is the mass flow rate information and
volume flow rate i-lro""~l;on Processing cir.;ui~ly 235, inslll~ing
microprocessor 236 together with memory elements 237 and 238,
operate in accordance with the present invention to provide highly
accurate density in.~ormation over a wide range of mass flow rates of
the material flowing through vibrating tubes 130. As subsequently
described in detail in connection with the flow charts of
Figures 4 and 5, this highly accurate density i~ol"~tion is derived by
the steps of me~llring the natural frequency of the vibrating tubes
from the signals provided by the velocity sensors 170, correcting this
measured natural frequency to compensate for the fact that the
me~llred natural frequency of tubes 130 decreases with increasing
mass flow rates thele~hlough, and using this corrected frequency in a
2û density calc~ tion to derive highly accurate density output data. This
density output data is of far greater accuracy than would be the case
if the me~llred natural frequency, rather than the corrected natural
frequency, were used in the density c~ tion
Figure 6 discloses the invention of Figure 2 in simplified form.
Corresponding elements on Figures 2 and 6 have identic~l reference
numbers to f~ilit~te an underst~ntling of the system of Figure 6.
Figure 6 discloses the densimeter as comprising meter apparatus 10 on
the let which inrludçs flow tube 130, the left velocity sensor 170L, the
right velocity sensor 170R, driver 180, a~d RTD temperature
sensor 190. These elements are cormected over paths 165L, 185,
165R, and 195 to meter electronics 20. These elements perform the

WO 94/21999 2 15 9 0 9 ~ PCT/US93/02763
-19-
same functions as aL-eady described in connection with Figure 2.
Meter electronics 20 cc~ ,-ises the flow tube drive circuit 27 and the
flow measurement circuit 23 which fimction as described in connection
with Figure 2 to receive and send signals to and from meter a~alus
S 10. Meter electronics 20 receives these signals and generates high
accuracy density inform~tion for the material flowing in vibrating
tube 130.
The flow me~llrement circuit ~3 is shown in simplified form on
Figure 6 and co,ll~.ises a phase diffe-ence m~ llrement circuit 601
and a frequency m~cl~rement circuit 6C2. Phase difference
me~ rement circuit receives over path 165L and 165R the output of
the left and right sensors, and, in response thereto, generates various
information in~lll(ling the mass flow rate MR and volume flow rate
VR of the material ;ul-elllly flowing within tube 130. This MR and
VR i~ol.. alion is applied over path 603 to frequency correction
element 606. Frequency m~llrement circuit 602 receives the
temperature illfol...ation over path 195 and the output signal of the
right velocity sensor 170R over path 165R. In re*)onse to the receipt
of this information, frequency measurement circuit generates an
output Fm indicating the m~llred resonant frequency of vibrating
tube 130 as material flows therethrough. This output signal Fm is
applied over path 604 to the frequency correction circuit 606.
Frequency correction circuit 606 responds to the reception of the mass
flow rate MR, the volume flow rate VR, and the me~llred frequency
Fm and generates a corrected frequency output signal Fc which corrects
the mP~cllred frequency Fm to compensate for the fact that the
measured frequency Fm differs from the no flow natural frequency of
the tube 130 because of the mass flow rate of the material ~;ul~enlly
flowing within tube 130.
Corrected frequency Fc is applied together with other
information not shown on Figure 6 to density me~cllrement element

WO 94/2D99 2 ~ ~ ~3 Q 9 ~ PCTIUS93/02763
-20-
608 which generates accurate density illÇ~ tion for the m~teri~l
~;ullGllLly flowing within tube 130. The density inform~tion generated
by density m.o~cllrement element 608 iS of greater accuracy at large
mass flow rate con-litionc because it uses the corrected frequency Fc
S rather than the me~cllred frequency Fm in its density co~ ;onc.
The output signal of density m~llrement clement 608 is
applied over path 26 tO lltili7~tion means 29 which may either
comprise a meter for a visual display of the generated density
h~~ l;on or, al~el-laiively, may co.~.ylise a process control system
that is controlled by the density signal on path 26.
As illustrated in Figure 3, the natural frequency of an
oscill~ting tube decreases as the mass flow rate of the material flowing
through the tube inaeases. The data in Figure 3 is represenLaLive of
this effect for a given flow tube geometry and a flo,-ving m~teri~l
having co~;~l density. The actual slope of the curve will change for
di~eren~ flow tube geometries and dencities of fluids and is easily
ascertained by developing the co..~ l K3, discussed above. The
vertical axis of Figure 3 colles~onds to the first out of phase natural
frequency of the flowmeter. The hol~o,-Lal axis is labeled in pounds
per minute (lbs/min) of mass flow rate. The percentages are incll-~ed
to represent the commercially recommentled and useable flow range
of the preferred embo-lim~nt The 100% point is the recommen~le~l
operating range but the flowmeter may be operated up to the 200%
point if the user is not concerned with the resllltin~ pres~ule drop
across the meter. In the initial portion of the curve at low mass flow
rates, the natural frequency remains relatively collsL~. Howc;ver as
the mass flow rate increases towards and beyond the 100% rate, the
natural frequency decreases. This is the effect that the present
invention corrects so that an accllrate m~ lrement of the density of
the flowing material can be determined. The operation of the present

wo 94~21999 ~ ~ 5 9 o g o PCT/US93tO2763
inveIltion in correcting the natural frequency for this effect is shown
in Figures 4 and 5.
Figures 4 and 5 describe in flow chart form how
microprocessor 236 and memories 237 and 238 operate in colu~uLiug
S a corrected natural frequency of vibrating tubes 130 as well as the
density of the m~teri~l flowing through the tubes. This c(~ ;on
is done in a series of sequential time intervals tl - - - t8 shown on the
right side of Figures 4 and 5. The process begins in element 404 in
which microprocessor 236 rccei~,es input and setup i~o~ ation over
paths 401, 402, 403 and 405. This is done in time interval tl. The
pickoff signal RPO from the right velocity sensor 170R is applied to
the microprocessor over path 401. The pickoff signal LPO from the
left velocity sensor 170L is applied over path 402. The temperature
signal RTD is applied over path 403 and information representing
co~lanls Kl, K2, K3 is applied from memories 237 and 238 over
path 405. The inform~tion received by element 404 is applied during
time interval t2 over path 406 to element 407 ~Nhich determines the /~ t
or /~ phase at a given frequency i~o~ lion which, as previously
described, represents the p~ aly inflllence of the Coriolis forces as
material flows through the vibrating tubes. Signal 406 is also applied
to element 408 which me~llres the frequency of the output signals of
sensor elements 170. The output of element 408 is a signal
representing the m~ red natural frequency of tubes 130 with
material flow. This signal is applied over path 410 to element 419.
The function of this element is subsequently described.
The /~ t or 1~ phase at a given frequency il~olmalion generated
by element 407 is a~plied during time interval t3 over path 415 to
element 409 which filters this information to remove noise and
- lm~lesired frequency components. The output of element 409 is
applied during interval t3 over path 411 to element 412 which subtracts
the mechanical zero offset of the structure associated with tubes 130

WO 94/21999 PCT/US93/02763
-22-
from the /~ t signal provided to path 411. The output of element 412
is a corrected A t signal which is applied over path 413 to element 414
during interval t4 which collvc;lL~ the /~ t signal to a mass flow rate
represçnt~tion of the flowing m~teri~l This mass flow rate may be
expressed in terms of grams per second. The output of element 414
representing the mass ~low rate is applied during interval t3 over
path 416 to element 417 which calculates the volume flow rate of the
flowing m~teri~l by dividing the mass flow rate by the material density
from the previous m~cnrement cycle as fee~lb~ over path 418 from
element 524. The operation of elem~nt 524 is subsequently described.
The output of element 417 is the mass flow rate and volume flow rate
information and is applied over path 420 to çl~mçnt 419.
Element 419 receives the mass flow rate and volume flow rate
i~-rol"~ion over path 418 during interval t6 and ~d-lition~lly receives
the m~cnred natural frequency over path 410 from element 408. In
response to the receipt of this ;"rO, ...~t;on, element 419 coll~ules a
differential frequency Fc and a differential period TdifE colles~onding
to the differential frequency Fc. This differential frequency Fc
represents the amount by which the measured natural frequency on
path 410 must be corrected to ascertain the corrected natural
frequency of vibrating tube 130. This corrected natural frequen~y is
equal to the zero macs flow rate natural frequency of the tube. As
previously described, this correction is necçcc~ry because of the
relation~hir between the natural frequency and mass flow rate
in~lic~tecl in Figure 3 wherein it is shown that the me~cllred natural
frequency decreases 2S mass flow rate increases. This frequen~y
differential or correction is c~ ted by elem~nt 419 by multiplying
the period TM of the measured frequency by the volume flow rate
(VR) and by the mass flow rate (M~) and by co~L~L K3. This
relationship is shown in element 419 in terms of the tube period rather
t_an the tube frequency. However, as is well-known, the tube period

WO 94/21999 21~ 9 1) 9 i3 PCTIUS93/02763
and natural frequency bear a reciprocal rel~tion~hip to one another
with the period being equal to a co~ divided by the frequency.
The co~sLa~L K3 is equal to the tube period for a flow state minus the
tube period at a no flow state divided by the T~ow (the tube
S periodflO~,,)(MR)(VR). This GA~lGs~ion is
TPLOW- TNO FLOW
( Tp~,ow) t~Z) ( V~)
Element 419 applies an output signal representing the period
of the c~ te~l frequency diL~erenLial over path 421 to elemen~ 522
during period t7 which c~ tes a corrected tube frequency Fc and a
corrected tube period Tc. This corrected tube period Tc collesponds
10 to the corrected natural frequency Fc and is determined by combining
the period TM Of the measured frequency with the di~erenlial period
Tdiff colles~ollding to the diL~elellLial frequency c~ ted by element
419. The relationship wherein the di~erell~al period Tdiff is combined
with the m~c.lred period Tm is TC=TM(1-(VR)(MR))K3.
Element 522 applies an output signal representing the corrected
natural frequen~y of tubes 130 over path 523 to element 524 which,
during interYal t~, c~ tes the density of the flowing material using
the corrected frequency (period) information derived by element 522.
The expression used by element 524 to perform this c~ tion is

WO 94/21999 PCT/US93/02763
-24-
D (d) ( ( tcm) TC -Kl) +D
where
d = Dw - D~,
Dw = density of water
D, = density of air
5 tcm = temp coefficient of tube for m~ red frequency
Tc = tube peAod corrected
Kl = (tca)T"2
Ta = tube period for air--no flow
tca = temp coeffl-ient of tube for air calibration
K2 = (tcw)Tw2 - tca(Ta~2
tcw = temp coefflcient of tube for water calibration
Tw = tube peAod for water--no flow
The density inform~tion generated by ~lement 524 is applied
as feedback information over path 525 and path 418 to element 417
which c~ tes a mateAal volume flow rate of i",~ruved precision
using both the density inform~tion and the mass flow rate hLCo~ ation
as inputs. The density il rul",ation on path 425 is also eYterlsled to the
tili7~tion means 29.
It is to be expressly understood that the claimed invention is
not to be limite~l to the descAption of the preferred embodiment but
encompasses other modifications and alterations within the scope and
spiAt of the i~lvenlive concept.
For example, the physical embodiment of the vibrating CoAolis
effect tube structure need not be as shown herein on Figure 1 wherein
it is portrayed as a pair of substantially U-shaped tubes. This need
not be the case and, if desired, a single vibrating U-tube may be used.
Also, if desired, any vibrating tube densimeter, such as a straight tube
CoAolis ef~ect structure may be used. Also, the descAption herein has

WO 94/21999 2~ 1 5 9 ~ !9 0 PCT/US93/02763
described a sensor structure comprising a pair of sensors with the
sensor ouL~ being used to derive what is herein termed as /~t
information which is used by processing ~;h~ y to generate the mass
flow rate, volume ~low rate and other information required to generate
the output data for which the Coriolis meter is ~esigned to provide.
This /~ t techni~lue need not be used and, as is well-known in the art,
an ~mpli~ltle sensor may be used wherein the m~gnitlltl~ of the
Coriolis effect is proportional to the m~gnitll-le of the signal output of
the sensor. This m~gnitllfle along with other inform~tion is then used
to derive the mass flow rale, volume flow rate and other information
the meter is to provide.
In snmm~ry~ the principles of the present invention are not
limited for use with a double U-tube structur~ as shown. They may
also be used with a single U-tube, a subst~nti~lly straight vibrating
tube or of any other suitable tube structure known in the art.
Furthermore, the invention is not limited to its use in connoction with
A t type signal proces~ing~ but instead, may be used in systems where
the Coriolis force is e~iessed in terms of an ~mplitll~e signal.
Further, the material whose density is determined by the
method and apparatus of the present invention may include a liquid,
a gas, a ~Llule thereof, as well as any substance that flows such as
slurries of different types. The mass flow rate (MR) and volume flow
rate (VR) of the flowing m~te.ri~l may be generated by the apparatus
comprising the densimeter or, ~ltern~tively~ can be generated by
separate apparatus and applied to the densimeter of the present
invenhon.

Representative Drawing