## Abstrict A method and appartus for measuring volumetric flow through a duct
without knowing the viscosity of the fluid is provided. A dual rotor
turbine volumetric flow meter is operably connected to a duct having
fluid flowing therethrough. The dual rotor turbine has a temperature
gauge, a first rotor and a second rotor with at least one of said
first rotor and said second rotor having a non-linear response to
fluid flow. The dual rotor turbine volumetric flow meter is calibrated
by deriving a Roshko/Strouhal number curve therefor. During measurement,
a first rotor frequency and a second rotor frequency are determined.
The second rotor frequency is divided by the first rotor frequency
to derive a frequency ratio which is then used to calculate a combined
Roshko number. A combined Strouhal number is derived by using the
combined Roshko number in conjunction with the Roshko/Strouhal number
curve. The volumetric flow rate is calculated using the combined
Strouhal number.
## Claims What is claimed is:
1. A method of measuring volumetric flow through a duct without
knowing the viscosity of the fluid, the method comprising the steps
of: providing a dual rotor turbine volumetric flow meter connected
to a duct having fluid flowing therethrough, the dual rotor turbine
having a temperature gauge, a first rotor and a second rotor, at
least one of said first rotor and said second rotor having a non-linear
response to fluid flow, calibrating the dual rotor turbine volumetric
flow meter by deriving a Roshko/Strouhal number curve therefor,
determining a first rotor frequency and a second rotor frequency,
dividing the second rotor frequency by the first rotor frequency
to derive a frequency ratio, calculating a combined Roshko number
using the frequency ratio, determining a combined Strouhal number
using the combined Roshko number and the combined Roshko/Strouhal
number curve, calculating the volumetric flow rate using the combined
Strouhal number.
2. The method of claim 1 wherein the volumentric flow rate is calculated
using the equation q=(f.sub.1 +f.sub.2)/St.sub.c *(1+3a(T.sub.op
-T.sub.ref )), where q is the volumetric flow rate, St.sub.c is
the combined Strouhal number, f.sub.1 is the first rotor frequency,
f.sub.2 is the second rotor frequency, a=coefficient of linear expansion,
T.sub.op =operating temperature of the meter and T.sub.ref =reference
temperature of the meter.
3. The method of claim 1 wherein the combined Roshko number is
calculated using the equation Ro.sub.c =(f.sub.1 +f.sub.2)/v*(1+3a(T.sub.op
-T.sub.ref)).
4. A method of calculating a mass flow through a duct, the method
comprising the steps of: providing a dual rotor turbine volumetric
flow meter connected to a duct having fluid flowing therethrough,
the dual rotor turbine having a temperature gauge, a first rotor
and a second rotor, at least one of said first rotor and said second
rotor having a non-linear response to fluid flow, calibrating the
dual rotor turbine volumetric flow meter by deriving a Roshko/Strouhal
number curve therefor, determining a first rotor frequency and a
second rotor frequency, dividing the second rotor frequency by the
first rotor frequency to derive a frequency ratio, calculating a
combined Roshko number using the frequency ratio, determining a
combined Strouhal number using the combined Roshko number and the
Roshko/Strouhal number curve, calculating the volumetric flow rate
using the combined Strouhal number, providing a density meter connected
to the duct, the density meter determining the density of the fluid,
multiplying the density by the volumetric flow rate to calculate
the mass flow moving through the duct.
5. The method of claim 4 wherein the volumentric flow rate is calculated
using the equation q=(f.sub.1 +f.sub.2)/St.sub.c *(1+3a(T.sub.op
-T.sub.ref)), where q is the volumetric flow rate, St.sub.c is the
combined Strouhal number, f.sub.1 is the first rotor frequency,
f.sub.2 is the second rotor frequency, a=coefficient of linear expansion,
T.sub.op =operating temperature read by the temperature gauge and
T.sub.ref =reference temperature of the meter.
6. The method of claim 4 wherein the combined Roshko number is
calculated using the equation Ro.sub.c =(f.sub.1 +f.sub.2)/v*(1+3a(T.sub.op
-T.sub.ref)).
7. The method of claim 4 wherein the mass flow is calculated using
the equation M=q*.rho. where M=mass flow, q=volumetric flow rate
and .rho.=density.
8. The method of claim 4 wherein the density meter uses differential
pressures to determine the density.
9. The method of claim 8 wherein the density meter is a combination
of a pitot tube and wall static pressure measurements.
10. The method of claim 9 wherein the density meter determines
the density using the equation .rho.=(Pt-Ps)/(V.sup.2.sub.avg /K)
wherein .rho.=fluid density, Pt=total pressure, Ps=wall static pressure,
K=a proportionality constant, and V.sub.avg =q/A where q=volumetric
flow rate and A=cross sectional area of the duct.
11. The method of claim 10 further comprising the steps of deriving
a temperature versus density curve for the fluid, reading a fluid
temperature reading from the temperature gauge, extrapolating a
density from the temperature reading and the temperature versus
density curve.
12. An apparatus for calculating a mass flow through a duct, the
apparatus comprising: a dual rotor turbine volumetric flow meter
connected to a duct having fluid flowing therethrough, the dual
rotor turbine having a temperature gauge, a first rotor and a second
rotor, at least one of said first rotor and said second rotor having
a non-linear response to fluid flow, the dual rotor turbine volumetric
flow meter adapted to be calibrated with a Roshko/Strouhal number
curve therefor, the first rotor having a first frequency and the
second rotor having a second frequency, means for calculating a
frequency ratio by dividing the first rotor frequency by the second
rotor frequency, means for calculating a combined Roshko number
using the frequency ratio, means for calculating a combined Strouhal
number by using the combined Roshko number and the Roshko/Strouhal
number curve, means for calculating the volumetric flow rate by
using the combined Strouhal number, a density meter connected to
the duct, the density meter determining the density of the fluid,
means for calculating the mass flow moving through the duct by multiplying
the density by the volumetric flow rate.
13. The apparatus of claim 12 wherein the means for calculating
the volumentric flow rate uses the equation q=(f.sub.1 +f.sub.2)/St.sub.c
*(1+3a(T.sub.op -T.sub.ref)), where q is the volumetric flow rate,
S.sub.c is the combined Strouhal number, f.sub.1 is the first rotor
frequency, f.sub.2 is the second rotor frequency, a=coefficient
of linear expansion, T.sub.op =operating temperature read by the
temperature gauge and T.sub.ref =reference temperature of the meter.
14. The apparatus of claim 12 wherein the combined Roshko number
is calculated using the equation Ro.sub.c =(f.sub.1 +f.sub.2)/v*(1+3a(T.sub.op
-T.sub.ref)).
15. The apparatus of claim 12 wherein the means for calculating
the mass flow uses the equation M=q*.rho. where M=mass flow, q=volumetric
flow rate and .rho.=density.
16. The apparatus of claim 12 wherein the density meter uses differential
pressures to determine the density.
17. The apparatus of claim 16 wherein the density meter is a combination
of a pitot tube and wall static pressure measurements.
18. The apparatus of claim 17 wherein the density meter determines
the density using the equation .rho.=(Pt-Ps)/(V.sup.2.sub.avg /K)
wherein .rho.=fluid density, Pt=total pressure, Ps=wall static pressure,
K=a proportionality constant, and V.sub.avg =q/A where q=volumetric
flow rate and A=cross sectional area of the duct.
19. The apparatus of claim 18 further comprising the steps of deriving
a temperature versus density curve for the fluid, reading a fluid
temperature reading from the temperature gauge, extrapolating a
density from the temperature reading and the temperature versus
density curve.
## Description TECHNICAL FIELD
This invention relates generally to the field of turbine flow meters,
and, more particularly, to a method and apparatus for using volumetric
turbine flow meters to measure mass flow through the meter.
BACKGROUND OF THE INVENTION
It is often desireable to use a mass flow rate meter which provides
a weight per time period number of flow through a duct for use in
certain applications. The term "duct" as used in the present
application refers to any tube, conduit, pipe, or the like through
which a fluid flows.
One major market for such meters is the aircraft industry which
wants to have accurate mass flow rates for its aircraft. This allows
an aircraft to load the minimum weight of fuel for given flight
including an appropriate safety margin. If an aircraft loads more
than that minimum weight, it is essentially burning excess fuel
to transport that excess weight to its destination. Thus, there
is an incentive to provide accurate mass flow numbers for the aircraft
industry as well as other applications.
One method is to use two different flow meters to measure mass
flow. In one arrangement, a volumetric flow meter insensitive to
density is used in combination with a density sensitive meter which
is used to determine the density of the fluid. Once the density
is known, a relatively simple calculation using the volume flow
rate reading from the volumetric flow meter combined with the density
yields the mass flow rate. However, such a combination is subject
only to limited number of applications over a narrow range of conditions
because one or the other flow meter is also sensitive to a number
of secondary variables such as temperature, viscosity, and/or Reynolds
number.
Turbine meters are often used as the volumetric flow meter, but
such meters are very sensitive to the viscosity, temperature and
Reynolds number of the fluid being measured. FIG. 1 shows the classical
correlation curve of a standard turbine meter. The illustrated curve
graphs the meter frequency divided by the fluid kinematic viscosity
is a function of the meter frequency divided by the volumetric flow
rate. If a turbine meter is operated at varying temperatures thereby
varying the viscosity, the flow rate cannot be determined without
knowing that viscosity.
It should be noted that when a turbine meter is operating at a
given temperature on a specific fluid, it is not necessary to know
the viscosity as long as the turbine meter is calibrated at these
same conditions. Those skilled in the art will recognize that such
conditions are quite rare in the real world.
In most situations, the temperature will vary which, in turn, causes
the viscosity to vary as shown in FIG. 4. This variation does require
that the meter system be able to determine the viscosity of a given
fluid at a given temperature. Often, this is accomplished by using
reference tables which plot viscosity versus temperature for a specific
fluid. However, the actual viscosity of any given batch of fluid
can vary from the viscosity of another batch of the same fluid sufficiently
to negate the value of a reference table as is also shown in FIG.
4.
Other volumetric flow meters can be used in a similar fashion but
all suffer from the same deficiency as the turbine flow meter. In
addition, many other types of flow meters do not have sufficient
accuracy to be competitive with the better mass measuring devices.
With regard to density measurements, there are a number of meter
used including differential pressure meters such as orifice plates
and target meters which are all sensitive to temperature, viscosity
and Reynolds number. In addition, such meters are limited as flow
sensitivity is a function of the square root of the differential
pressure of force signals generated by the meters.
As a result of the problems using a volumetric flow meter and a
density meter combination, most current metering systems employ
direct mass flow measuring meters for such measurements. One example
of such a meter is a Coriolis meter which tend to be quite expensive.
However, when direct mass flow measurement is desired, the user
has few choices.
Another direct flow meter employs two turbine elements in tandem
wherein one turbine element employs straight turbine blades while
the second meter uses a more conventional curved design. The two
elements are coupled using a torsional spring. As the mass flow
rate increases, the torque reaction causes a phase shift between
the two blades. The phase shift is a function of the mass flow rate
as long as the rotational speed of the two elements is constant.
Several designs are used to maintain the constant rotational speed,
including a synchronous motor and a centrifugally loaded vane set.
These meters, while commonly used in fuel measurements, are not
very accurate and are relatively expensive. Thus, there is a need
for a more accurate and less expensive method of measuring mass
flow.
The present invention meets this need.
SUMMARY OF THE INVENTION
It is an object of this invention to provide an improved mass flow
metering system which is accurate and inexpensive.
Further objects and advantages of the invention will become apparent
as the following description proceeds and the features of novelty
which characterize this invention will be pointed out with particularity
in the claims annexed to and forming a part of this specification.
BRIEF DESCRIPTION OF THE DRAWINGS
The present invention may be more readily described by reference
to the accompanying drawings in which:
FIG. 1 is a graph showing a typical universal viscosity curve for
a turbine meter;
FIG. 2 shows a typical Strouhal Number versus Roshko Number correlation
plot for a dual rotor turbine meter;
FIG. 3 shows a graph of a dual rotor turbine meter frequency ratio
as a function of the Roshko number for an untrimmed rotor;
FIG. 4 plots a typical fluid viscosity versus temperature curve;
FIG. 5 plots the Strouhal number using a frequency ratio, each
as a function of Roshko Number for a dual rotor meter that has not
been trimmed;
FIG. 6 plots the dual rotor turbine meter frequency ratio as a
function of the Roshko number for a meter that has been adjusted
to a non-linear relationship;
FIG. 7 plots Strouhal number using frequency ratio for the adjusted
non-linear meter, each as a function of the Roshko Number for a
dual rotor meter that has been trimmed to be non-linear;
FIG. 8 is a graph demonstrating fluid density versus temperature
with a normal upper and a normal lower limit;
FIG. 9 shows the technique for trimming a rotor; and
FIG. 10 shows the assembly of a mass flow meter.
DESCRIPTION OF THE PREFERRED EMBODIMENT
The present invention employs a dual rotor turbine meter 10 described
in U.S. Pat. No. 5689071 entitled "Wide Range, High Accuracy
Flow Meter" which issued on Nov. 18 1997 to Ruffner and Olivier
(the present applicant) which is herein incorporated by reference
and is illustrated in FIG. 10. U.S. Pat. No. 5689071 describes
the operation of two counter rotating hydraulically coupled rotors
18 20 in a single housing. While operating in many respects like
a conventional turbine meter, the patented meter has superior properties
in others. Specifically, the operating range is greatly extended.
Further, by monitoring the output frequency of both rotors 18 20
self-diagnostics can be performed.
As described in U.S. Pat. No. 5689071 the Roshko Number and
the Strouhal Number are used in the calculation of the volumetric
flow rate as follows. The Roshko numbers for each rotor are:
where: f.sub.1 =output frequency of rotor 1 (18) f.sub.2 =output
frequency of rotor 2 (20) v=kinematic viscosity of the fluid at
T.sub.op a=coefficient of linear expansion of the material making
up the body of the meter, for example, 300 series stainless steel
T.sub.op =operation temperature from a temperature gauge 16 of meter
T.sub.ref =reference temperature of the meter (may be any convenient
temperature).
The Combined Roshko number Ro.sub.c is defined as:
and the Strouhal numbers for each rotor are:
where: q=volumetric flow rate and the other terms are as defined
previously.
The Combined Strouhal number St.sub.c is defined as follows:
or, alternatively, instead of the sum of the frequencies, an average
of the frequencies can be employed which is one half the value given
above.
The relationship between the Strouhal and Roshko numbers is determined
during calibration of the meter by deriving a graph such as shown
in FIG. 2. As shown in FIG. 2 rotor 1 data taken at 1 centistoke
viscosity 15 forms a continuous curve with rotor 1 data taken at
8.3 centistoke viscosity 16 and rotor 2 data taken at 1 centistoke
viscosity 19 forms a continuous curve with rotor 2 data taken at
8.3 centistoke viscosity 20. The average combined rotor 1 and rotor
2 data at 1 centistoke viscosity 17 forms a continuous curve with
the combined rotor 1 and rotor 2 data at 8.3 centistoke viscosity
18. When using the meter, the Roshko number is determined by measuring
the frequency of a rotor, determining the kinematic viscosity as
described in detail below, measuring the operating temperature and
then solving the above equation.
Next, the Strouhal number is computed from the calibration curve
of FIG. 2. Solving the Strouhal number equations for the volumetric
flow rate yields:
where: St.sub.c =combined Strouhal number (or average)
A typical Strouhal number versus Roshko number curve for a two
rotor system is shown in FIG. 2 along with a combined Strouhal number
(St.sub.c) curve. Note that the curves are non-linear with rotor
1 tending to have a declining Strouhal number (St.sub.1) as its
Roshko number (Ro.sub.1) decreases and rotor 2 tending to have an
increasing Strouhal number (St.sub.2) as its Roshko number (Ro.sub.2)
increases over most of its range. At lower values, both curves decline.
A review shows that there is little or no Roshko number range where
either rotor is very linear. However, the combined (average) Strouhal
number (St.sub.c) is much more linear, at least at the higher Roshko
numbers.
It should be noted that it is not possible to directly determine
the Roshko number without knowing both the rotor frequencies (f.sub.1
and f.sub.2) and the operating kinematic viscosity (v) of the fluid.
Of course, the rotor frequencies (f.sub.1 and f.sub.2) are measured
and usually the kinematic viscosity (v) of the fluid is predetermined
as a function of operating temperature (T.sub.op). Thus, if the
operating temperature (T.sub.op) is known, the kinematic viscosity
(v) is also known.
If the fluid is water, the viscosity versus temperature curve is
reliably obtainable from textbooks and other sources. The viscosity
values of pure water do not vary much, if at all, from the values
in published temperature/viscosity charts.
However, the viscosity versus temperature relationship for other
fluids, for example, hydrocarbons including jet fuel and gasoline,
should be empirically determined for each batch of fluid used. The
viscosity/temperature relationship can vary greatly from one batch
to another depending upon such factors as the origin, manufacturer
and constituents of each batch. It is quite common for the viscosity
of a given fluid to vary as much as .+-.10% from one batch to another
at a constant temperature as shown graphically in FIG. 4 which plots
textbook data 25 with upper and lower limits 24. Since the Strouhal
number versus Roshko number curve in non-linear, such 10% changes
can yield a significant change in the Strouhal number for a given
output frequency (f). If the viscosity used in the calculation were
in error by this amount, then the calculated volumetric flow rate
will also be inaccurate. Thus, such variations often make textbook
or published chart numbers 25 impractical sources for the viscosity.
However, creating a temperature/viscosity curve for each and every
batch of fluid is often impractical or at least very laborious.
However, if the frequency ratio (f.sub.2 /f.sub.1) is considered
as a function of the combined Roshko number (averaged number) as
shown in FIG. 3 it is shown that at any given value of Ro.sub.c,
a different frequency ration exists. Then, using FIG. 2 a unique
St.sub.c number corresponding to the combined Roshko number (Ro.sub.c),
can be derived. Thus, for a given volumetric flow rate, the combined
frequency (f.sub.1 +f.sub.2) remains constant as the viscosity changes,
but the frequency ratio (f.sub.2 /f.sub.1) will vary. Conversely,
for any given value of the combined frequency (f.sub.2 +f.sub.1),
a unique frequency ratio (f.sub.2 /f.sub.1) will exist for any value
of kinematic viscosity.
In conclusion, as best seen in FIG. 5 the use of the two relationships
(f.sub.2 +f.sub.1) and (f.sub.2 /f.sub.1) eliminates the need to
know the kinematic viscosity of the fluid. A close examination of
a curve 26 illustrated in FIG. 5 shows that for any combined frequency
(f.sub.2 +f.sub.1), a unique value of combined Strouhal number (St.sub.c)
exists for any given value of kinematic viscosity. It is also shown
that for any given value of frequency ratio (f.sub.2 /f.sub.1),
a unique combined Roshko number (Ro.sub.c) also exists. Thus, by
simply knowing both frequencies (f.sub.2 and f.sub.1), these numbers
may be obtained without reference to the kinematic viscosity, thereby
eliminating the need to pre-determine or measure the kinematic viscosity
versus temperature relationship for each batch of fluid.
Those skilled in the art are aware that often turbine meters including
the dual rotor turbine meter are designed to have as linear a response
as possible. However, in the present invention, a perfectly linear
response must be avoided. It will be obvious that the f.sub.2 /f.sub.1
relationship and the curves derived function only if the individual
curves of Strouhal number verses Roshko number shown in FIG. 2 are
non-linear.
A best seen in FIG. 5 the curve 26 frequency ratio is flat at
the higher Roshko numbers. It is difficult to use this portion of
the curve 26 to isolate the operating Roshko number. A technique
which uses the frequency sum and the nominal value of the viscosity
at the current operating temperature (T.sub.op) 27 can be used to
isolate the band in which the correct Roshko number will fall.
First, compute the frequency sum (f.sub.1 +f.sub.2) and use the
nominal value of kinematic viscosity at the operating temperature
27 from textbook data 25 similar to FIG. 4 to determine the corresponding
Roshko number for that summation. A graph 27 of the results is provided
in FIG. 5 as well as an error band 28 showing the potential error
arising from this computation. However, since the Strouhal number
versus Roshko number is relatively flat in the range where the frequency
ratio curve is also flat, the resulting error in Strouhal number
is relatively small and acceptable in many cases.
The above computation is more accurate if the individual curves
of Strouhal number versus Roshko number and the resulting Roshko
number versus frequency ratio are non-linear. Care must be taken
in the design of the turbine meter to assure that non-linear characteristics
are preserved throughout the range of interest. In the case of the
dual rotor turbine meter, this is accomplished by designing at least
one of the two rotors to have the value of the frequency ratio change
continually as a function of the Roshko number.
However, in many meter designs, it is desireable to have the frequency
ratio versus Roshko number curve as linear as possible. If this
is the case, the above computation may still be applicable though
the user must be aware of the added uncertainty in the values obtained.
There are a number of techniques to providing a rotor with a non-linear
response, namely, changing the chord, changing the axial length
of a rotor or by changing the blade shape. One simple way is shown
in FIG. 9 which trims the corners of the rotor blade. If a user
wishes to raise the Strouhal number at higher Roshko numbers, trimming
a corner C effectively shortens the chord on the pressure side of
the blade thereby producing the desired effect.
The results of trimming the first rotor are shown in FIGS. 6 and
7. As can be observed, the entire plot has a usable slope over the
entire range since 1 centistoke viscosity points 30 form a continuous
curve with 8.3 centistoke viscosity points 31 and it is no longer
necessary to calculate the results by determining the viscosity
of the fluid. Thus, the meter is now totally insensitive to viscosity
because the Roshko-number can be determined without reference thereto
as shown in FIG. 7 where the frequency ratio versus Roshko Number
curve 32 leads directly to the Strouhal Number in curve 33 again
without reference to viscosity. Note that calibration and verification
of the meter can be done by actually verifying the operating viscosity
and comparing the results to the nominal values to avoid large errors
entering the system from momentary invalid readings.
It will also be obvious to those skilled in the art that considerable
mathematical calculations are required to practice this method.
While hand calculations are certainly possible, the use of a computer
or microprocessor makes this solution quite practical and relatively
inexpensive.
It will be apparent to those skilled in the art that the above
minimizes the variation in volumetric measurements due to secondary
variables, i.e., the temperature, viscosity and Reynolds number.
The reduction in variation makes it practical to consider use of
the dual rotor meter in combination with a density sensor to determine
the mass flow rate through a duct such as a fuel supply line. It
is noted that dual rotor turbine meters are generally insensitive
to pressure variations. Thus, the use of a which measures differential
pressures to determine the density is a good choice as it avoids
cross sensitivities between the two meters.
There are a number of meters which use differential pressures,
including, but not limited to, measuring the differential pressure
across an orifice, across a blunt body, across a rotor, with a pitot
tube or using a wall static method. A target meter could similarly
be used.
However, measuring flow rates with a target meter, or by using
an orifice, or across a blunt body and across rotors are all sensitive
to Reynolds numbers and fluid density. Since the kinematic viscosity
is assumed to be unknown (although it can be mathematically determined)
in the dual rotor meter discussed previously, using such methods
essentially defeats the purpose of same, namely, the elimination
of viscosity as a variable.
Thus, one preferred method of computing density is the use of a
pitot tube and wall static. FIG. 10 shows a dual rotor meter 10
with a pitot tube 12 and wall static 14 installed. As is well known
in the art, pitot tube 12 is used to calculate the velocity of the
fluid as:
where: V=fluid velocity at the point of Pt measurement Pt=total
pressure Ps=wall static pressure .rho.=operating fluid density or
conversely stated:
The density will change with temperature, but the differential
pressure will change proportionally. Thus, the operating density
is determined independently of other variables. At this point, the
dual rotor turbine meter has determined the volumetric flow rate
and the pitot tube/wall static have isolated the density, both independently
of secondary variables. Further, the average velocity in the duct
is computed as:
where: A=cross sectional area of the duct.
The velocity measured by the pitot tube is local or point velocity
while the velocity computed from the flow rate is an average velocity.
A proportionality constant K is added to the equations to handle
this difference and thus the density equation is modified as follows:
The proportionality constant K may actually vary somewhat with
V.sub.avg or q but is easily determined at calibration. The density
equation is restated as:
and the mass flow rate is:
To summarize, the use of the present method which measures only
rotor frequencies f.sub.1 and f.sub.2 in combination with a pitot
tube and wall static differential pressure is ideally suited for
determining a mass flow rate through a duct.
One of the major advantages for use of a dual rotor turbine meter
is the wide operating range, or turndown, of such meters. However,
one of the major disadvantages of the pitot tube/wall static port
is the small operating range of same. As shown above, the velocity
measured in a pitot tube is a function of the square root of the
differential pressure and density. Thus, for a 16:1 change in differential
pressure, only a 4:1 change in flow rate is achieved. Since pressure
transducers are normally rated as a percentage of full scale, a
16:1 ratio is generally all that can be tolerated. Note that there
are methods to extend this limit, such as stacked differential pressure
devices, or simply accepting a reduced accuracy in an extended range.
However, another solution is also possible with particular application
to hydrocarbon fluids such as jet fuel.
As noted previously, the density versus temperature curve for most
hydrocarbon fluids changes significantly from one batch to another.
In most applications, the batch of fluid on which the meter is employed
is changed periodically. However, once operation of the system is
limited to a particular batch of fluid, the change in density is
a simple function of temperature (and pressure to a lesser degree
in high pressure applications).
As an example, consider the application in a fuel supply line in
a jet aircraft. The engine is started and operated at idle, usually
a very low flow rate. The engine is then accelerated to near maximum
at takeoff for a relatively short period of time. Once airborne,
the engine is throttled back to a cruise flow rate which is maintained
for a long period of time, relatively speaking. This cruise flow
rate is well within the 4:1 range of maximum flow rate. During descent
and landing, the flow rate is reduced again to a lower value for
a short time, and then returns to idle before shutdown. The total
amount of fuel used during the idle and landing times is very small
compared to the takeoff and cruise periods. Note that this scenario
also applies to a number of other applications.
A density versus temperature curve 34 for a typical hydrocarbon
fluid is shown in FIG. 8. Over a normal operating range, the density
change can be linearly approximated as temperature changes. Also
seen in FIG. 8 are batch to batch limits 35 36 for a typical hydrocarbon
fluid. A temperature versus density curve 39 for any given batch
of hydrocarbon fluid is parallel to the typical curve 34 but offset
from same by some small quantity. Thus, once a single density/temperature
point is determined for a specific batch of hydrocarbon fluid, the
temperature/density curve 39 can be extrapolated from same to cover
the expected operating range. Other subsequent measurements of density
at other temperatures can be combined to create a composite curve
38 of the entire operating cycle as the flow rate and temperature
achieve the operating condition.
Thus, at flow rates outside the optimum range for a pitot tube,
the density measurement may be extrapolated from previously obtained
data. The density data for a particular batch of fluid is maintained
and accumulates, subject to data storage limitations, until a new
batch arrives. Once a new batch arrives, the data is purged and
new data added to allow for accurate extrapolation outside the operating
range of the pitot tube. Until enough data is accumulated to make
an accurate extrapolation, textbook averages can be used as temperature/density
measurements.
FIG. 8 show the typical accumulation of density data during the
operation of the system. A running average, standard deviation computation
or other form of limiting the very large number of data points may
be used if needed to keep the data from overwhelming the processor.
Each time a new batch of fluid is used the data buffer is reset
and new data accumulated. For an initial startup, or after a reset,
textbook or nominal data for a particular fluid is used until sufficient
data is accumulated to more precisely determine the true curve of
density versus temperature for that new batch.
With this method of density determination, the current operating
temperature is actually used to determine the density from the defined
curve. The measured density points are used only to continually
define the temperature versus density curve.
Although only certain embodiments have been illustrated and described,
it will be apparent to those skilled in the art that various changes
and modifications may be made therein without departing from the
spirit of the invention or from the scope of the appended claims. |