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 operably
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 operably 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 Rosbko/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 operably
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
operably 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 operably 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+3-
a(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.
14. The apparatus of claim 12 wherein the combined Roshko number
is calculated using the equation (see inquiry above).
15. The method 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 method of claim 12 wherein the density meter uses differential
pressures to determine the density.
17. The method of claim 16 wherein the density meter is a combination
of a pitot tube and wall static pressure measurements.
18. The method 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 method 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
[0001] 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
[0002] 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.
[0003] 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.
[0004] 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.
[0005] 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.
[0006] 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.
[0007] 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.
[0008] 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.
[0009] 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.
[0010] 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.
[0011] 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.
[0012] The present invention meets this need.
SUMMARY OF THE INVENTION
[0013] It is an object of this invention to provide an improved
mass flow metering system which is accurate and inexpensive.
[0014] 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
[0015] The present invention may be more readily described by reference
to the accompanying drawings in which:
[0016] FIG. 1 is a graph showing a typical viscosity curve;
[0017] FIG. 2 shows a correlation plot for a dual rotor meter;
[0018] FIG. 3 shows a graph of frequency ratio as a function of
the Roshko number;
[0019] FIG. 4 plots a typical viscosity versus temperature curve;
[0020] FIG. 5 plots the Strouhal number using a frequency ratio;
[0021] FIG. 6 plots the frequency ratio as a function of the Roshko
number for a meter that has been adjusted to a non-linear relationship;
[0022] FIG. 7 plots Strouhal number using frequency ratio for the
adjusted non-linear meter;
[0023] FIG. 8 is a graph demonstrating a density data collection
technique;
[0024] FIG. 9 shows the technique for trimming a rotor; and
[0025] FIG. 10 shows the assembly of a mass flow meter.
DESCRIPTION OF THE PREFERRED EMBODIMENT
[0026] The present invention employs the dual rotor turbine meter
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. U.S. Pat. No. 5689071 describes the operation of
two counter rotating hydraulically coupled rotors 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, self-diagnostics can be performed.
[0027] 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:
Ro.sub.1=f.sub.1/v*(1+2a(T.sub.op-T.sub.ref))
Ro.sub.2=f.sub.2/v*(1+2a(T.sub.op-T.sub.ref))
[0028] where:
[0029] f.sub.1=output frequency of rotor 1
[0030] f.sub.2=output frequency of rotor 2
[0031] v=kinematic viscosity of the fluid at T.sub.op
[0032] a=coefficient of linear expansion of the material making
up the body of the meter, for example, 300 series stainless steel
[0033] T.sub.op operating temperature of the meter
[0034] T.sub.ref reference temperature of the meter (may be any
convenient temperature).
[0035] The Combined Roshko number Ro.sub.c is defined as:
Ro.sub.c=(f.sub.1+f.sub.2)/v*(1+3a(T.sub.op-T.sub.ref))
[0036] and the Strouhal numbers for each rotor are:
St.sub.1=f.sub.1/q*(1+3a(T.sub.op-T.sub.ref))
St.sub.2=f.sub.2/q*(1+3a(T.sub.op-T.sub.ref))
[0037] where:
[0038] q=volumetric flow rate and the other terms are as defined
previously.
[0039] The Combined Strouhal number St.sub.c is defined as follows:
[0040] St.sub.c=(f.sub.1+f.sub.2)/q*(1+3a(T.sub.op-T.sub.ref))
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.
[0041] 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. 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.
[0042] Next, the Strouhal number is computed from the calibration
curve of FIG. 2. Solving the Strouhal number equations for the volumetric
flow rate yields:
q=(f.sub.1+f.sub.2)/St.sub.c*(1+3a(T.sub.op-T.sub.ref))
[0043] where:
[0044] St.sub.c=combined Strouhal number (or average)
[0045] 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.
[0046] 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.
[0047] 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.
[0048] 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. 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 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.
[0049] 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.
[0050] 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 the curve 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.
[0051] 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 versus Roshko number shown in FIG. 2 are
non-linear.
[0052] As best seen in FIG. 5 the curve of frequency ratio is
flat at the higher Roshko numbers. It is difficult to use this portion
of the curve 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) can be used to isolate
the band in which the correct Roshko number will fall.
[0053] First, compute the frequency sum (f.sub.1+f.sub.2)and use
the nominal value of kinematic viscosity at the operating temperature
from data similar to FIG. 4 to determine the corresponding Roshko
number for that summation. A graph of the results is provided in
FIG. 5 as well as an error band 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.
[0054] 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.
[0055] 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.
[0056] 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.
[0057] The results of trimming the first rotor are shown in FIG.
6. As can be observed, the entire plot has a usable slope over the
entire range 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. 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.
[0058] 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.
[0059] 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.
[0060] 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.
[0061] 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.
[0062] 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:
V=[(Pt-Ps)/.rho.].sup.1/2
[0063] where:
[0064] V=fluid velocity at the point of Pt measurement
[0065] Pt=total pressure
[0066] Ps=wall static pressure
[0067] .rho.=operating fluid density
[0068] or conversely stated:
.rho.=(Pt-Ps)/V.sup.2
[0069] 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:
V.sub.avg=q/A
[0070] where:
[0071] A=cross sectional area of the duct.
[0072] 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:
.rho.=K*(Pt-Ps)/V.sup.2
[0073] 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:
.rho.=(Pt-Ps)/(V.sup.2.sub.avg/K)
[0074] and the mass flow rate is:
M=q*.rho.
[0075] 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.
[0076] 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.
[0077] 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).
[0078] 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. The
density versus temperature curve for a typical hydrocarbon fluid
is shown in FIG. 8.
[0079] Over a normal operating range, the density change can be
linearly approximated as temperature changes. Also seen in FIG.
8 are the batch to batch limits for a typical hydrocarbon fluid.
The temperature versus density curve for any given batch of hydrocarbon
fluid is parallel to the typical curve 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 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 of the entire operating
cycle as the flow rate and temperature achieve the operating condition.
[0080] 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.
[0081] 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.
[0082] 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.
[0083] 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. |