Abstrict Elbow mass flow meter. The present invention includes a combination
of an elbow pressure drop generator and a shunt-type mass flow sensor
for providing an output which gives the mass flow rate of a gas
that is nearly independent of the density of the gas. For air, the
output is also approximately independent of humidity.
Claims What is claimed is:
1. An apparatus for measuring mass flow in gases which comprises
in combination:
an elbow in which turbulent flow of the gas to be investigated
is established, said elbow including a first straight leg and a
second straight leg, the first straight leg being located upstream
from the second straight leg, and having a first sampling port therein
and the second straight leg having a second sampling port therein;
and
a shunt-type mass flow sensor having an input port and an output
port, the input port being attached to the first sampling port and
being adapted to receive a portion of the turbulent flow from said
elbow, and the output port thereof being attached to the second
sampling port such that after flowing through said mass flow sensor,
the portion of the turbulent flow entering said flow sensor is returned
to said elbow.
2. The gas flow measuring apparatus as described in claim 1 wherein
said shunt-type mass flow sensor is a laminar flow thermal anemometer.
3. The gas flow measuring apparatus as described in claim 1 wherein
said elbow is mitered, whereby turbulent flow is established therein.
4. A method for measuring mass flow in gases which comprises the
steps of:
establishing turbulent flow of the gas to be investigated in an
elbow, the elbow including a first straight input leg and a second
straight output leg;
diverting a small portion of the gas entering the input leg of
the elbow into a shunt-type mass flow sensor; and
returning the gas passing through the flow sensor to the output
leg of the elbow.
Description In industrial and scientific applications, it is frequently necessary
to measure the flow rate of gases. Often, the space devoted to the
flow meter and its related flow tubing is not of consequence; however,
there are situations in which the space is limited as, for example,
within the confines of a scientific instrument. Moreover, with scientific
apparatus there is generally a need for an electrical analog output
from a flow meter. Typically, scientific apparatus will have on-board
electronic capabilities for data acquisition, handling and display
which may not only justify the need for an electrical analog output
from the flow meter, but may necessitate it. There are industrial
situations for which the mass flow rate of gases is needed and for
which the pressure drop across the flow meter is of concern because
of power consumption considerations.
It is known that the pressure drop across an elbow can be used
to measure volumetric flow rates since the pressure drop is proportional
to the dynamic head of gas flowing through the elbow. See, e.g.,
E. G. Hauptmann, "Take A Second Look At Elbow Meters For Flow
Monitoring," Instruments and Control Systems, October, 1978
pages 47-50. Indeed, the author believes that such meters can be
considered a primary flow measuring device and a practical alternative
to orifice plates and venturis. In addition, shunt-type mass flow
meters have been used to measure the flow rate across linear laminar
flow elements. However, the use of a combination of these two technologies
has not been described.
There are three companies which manufacture devices which will
measure small mass flow rates of gases. A first uses a configuration
which requires that the gas must first flow through a flow straightener
(long section of straight pipe) before entering the actual flow
measurement device. Within the device is a laminar flow element,
which produces a pressure drop linear with the flow rate, and governed
by the Poiseuille relationship. The pressure drop created by the
laminar element flow causes a shunt flow to pass through a thermal
anemometer. This flow is also laminar as a result of the dimensions
of the tubing and the flow rate through the shunt. As a consequence,
there is a direct proportionality between the flow rate through
the laminar flow element and the flow rate through the shunt. Since
the fluid properties of the fluid which flows through the laminar
element and that which flows through the shunt are the same, and
since the thermal anemometer measures the mass flow rate through
the shunt, the electrical analog signal can be calibrated in terms
of the overall mass flow rate through the device. The principal
disadvantage of this system is that it is bulky due to the need
for obtaining laminar flow in the main restriction. In turn, this
necessitates a long, straight section of tubing upstream and downstream
of the body of the flow meter. For a unit designed for a flow rate
range of 0-100 L/min, the overall length of the meter is 14.2 in.
(360 mm). A second device does not have a shunt flow, but rather
has a thermal anemometer placed in a straight pipe, where the overall
tube length is approximately 11 times the internal diameter of the
pipe. For example, such a system designed for a flow rate range
of 0-3 cfm (0-85 L/min) would require an overall length of approximately
11 in. (279 mm) for the meter. This meter would be more sensitive
to upstream flow conditions than the meter described above, since
passages in the laminar flow element of that system would eliminate
any swirl in the flow. The added pressure resistance of the laminar
flow elements would also tend to smooth the velocity profile across
the tube cross section. The second meter may not have a sufficiently
long approach tube. Experiments have shown that more than 40 pipe
diameters are required for the complete mixing of a trace gas into
a carrier gas. Since mass and momentum mix similarly in a flow,
assurance of a constant velocity profile would be obtained only
if the length of the approach tube were approximately 40 tube diameters.
The ratio of entrance length to tube diameter for that device is
approximately 16.
A third apparatus employs an orifice in the main flow passage and
a laminar flow element as a shunt across the orifice. A screw is
driven into the orifice to produce the pressure differential needed
to cause the proper flow through the shunt mass flow meter. The
combined orifice and thermal anemometer provide a readout that is
proportional to mass flow rate; however, each unit must be separately
calibrated. Also, if the screw setting is changed in maintenance,
or if the screw should move as a consequence of vibrations or other
phenomena, the unit will give an erroneous output signal.
Accordingly, it is an object of the present invention to provide
an apparatus for measuring the mass flow rate of a turbulent gas
through pipes or tubes.
Another object of the invention is to provide an apparatus for
measuring the mass flow rate of a turbulent gas through pipes or
tubes without significant loss in pressure in the pipe or tube.
Additional objects, advantages and novel features of the invention
will be set forth in part in the description which follows, and
in part will become apparent to those skilled in the art upon examination
of the following or may be learned by practice of the invention.
The objects and advantages of the invention may be realized and
attained by means of the instrumentalities and combinations particularly
pointed out in the appended claims.
SUMMARY OF THE INVENTION
To achieve the foregoing and other objects, and in accordance with
the purposes of the present invention, as embodied and broadly described
herein, the apparatus for measuring mass flow in gases of this invention
may comprise in combination: an elbow in which turbulent flow of
the gas to be investigated is established, the upstream leg thereof
having a sampling port therein and the downstream leg also having
a sampling port therein; and a shunt-type mass flow meter having
its input port attached to the upstream sampling port of the elbow
for receiving a portion of the turbulent flow from the elbow, and
its output port being attached to the downstream sampling port of
the elbow such that after flowing through the mass flow meter, the
portion of the turbulent flow entering the flow meter is returned
to the elbow.
Benefits and advantages of the present invention include an alternative
to other types of flow metering devices such as obstruction meters
(nozzles, venturis, and orifices) or rotameters, for situations
where the flow is turbulent. The subject elbow mass flow meter is
scalable from small-sized devices with flow rates of only a few
cfm to large devices with flow rates of hundreds of thousands of
cfm. Moreover, once the elbow is calibrated, recalibration is unnecessary
since the loss coefficient remains constant under turbulent flow
conditions. Since shunt meters require periodic recalibration, this
is of particular importance for large systems, since the part of
the mass flow meter that would need calibration is only approximately
1 in. in size.
BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are incorporated in and form a
part of the specification, illustrate an embodiment of the present
invention and, together with the description, serve to explain the
principles of the invention. In the drawings:
FIG. 1 shows a schematic representation of the apparatus of the
present invention illustrating, in particular, the combination of
the elbow and the mass flow sensor to measure the mass flow rate
of a gas.
FIG. 2 shows a schematic representation of an existing volumetric
flow metering apparatus utilizing an elbow and a pressure sensing
apparatus.
FIG. 3 shows a calibration curve for the subject flow meter.
DETAILED DESCRIPTION OF THE INVENTION
Briefly, the present invention includes an elbow pressure drop
generator together with a mass flow sensor for measuring the mass
flow rate of gases. There is only a small pressure drop across the
elbow, and an electrical analog output signal is generated by the
mass flow sensor. The subject apparatus includes an elbow with a
by-pass (shunt) mass flow sensor. Turbulent flow is established
through the elbow, and flow through the by-pass tubing is laminar.
As gas flows through the elbow, there is a pressure loss across
the elbow which is enhanced by the mitered form of the elbow.
The invention utilizes turbulent flow in the main stream through
an elbow and laminar flow in the shunt stream through a mass flow
sensor. Turbulent flows are associated with larger flow rates which
implies that the diameter of the flow cross-section of a device
in which the flow is turbulent will be smaller than if the flow
is laminar. For the elbow meter of the present invention, the length
is only 3.2 in. (81 mm) as compared with the first commercial apparatus
described above, which operates with the main flow in the laminar
regime in order to provide a linear relationship between the main
flow and the shunt flow, and has a length of 13.8 in. (360 mm).
Even though the second commercial apparatus described above can
operate in the turbulent regime, it must have a well-developed profile
at the entrance of the sensing region in order to infer the flow
rate through the tube from an anemometer reading at a single point
in the flow. This is achieved through the use of long tubes on the
upstream and downstream sides of the anemometer. The third commercial
device described above utilizes a mass flow meter which measures
flow shunted across an orifice. It employs a screw driven into the
flow to create the appropriate resistance. This system would not
be practical for measurement of large flows due to the need to calibrate
each combination of orifice and screw configuration. Without a screw,
a well-designed orifice meter causes about twice the pressure loss
as an elbow meter.
Reference will now be made in detail to the present preferred embodiments
of the invention, examples of which are illustrated in the accompanying
drawings. Similar or identical structure is identified by identical
callouts. Turning now to the drawings, FIG. 1 shows a schematic
representation of the apparatus of the present invention, showing
the combination of an elbow to generate a pressure drop related
to the primary flow therein and a mass flow sensor to generate an
electrical signal, based on a portion of the total flow shunted
through it, which can be calibrated to accurately measure the mass
flow of gas entering the elbow. Gas flow enters elbow 10 at opening
12 and passes first sampling port 14. A portion of the gas flows
through sampling port 14 and input shunt tube 16 and into a laminar
flow thermal anemometer mass flow sensor 18. After passing through
the anemometer, the gas is returned to the flow in the elbow at
second sampling port 20 through exit shunt tube 22. The gas flow
exits elbow 12 through opening 24. The pressure is higher at port
14 than at port 20 due to flow separation and other flow losses
in the elbow; and, as a consequence, when the two points are connected
by a shunt tube, this pressure difference will cause there to be
a flow of gas through the shunt tube. The output from mass flow
sensor 18 which gives an electrical analog output related to the
mass flow rate through the shunt tube, which in turn, is related
to the mass flow rate through the elbow, is directed to signal processor
26 for linearization and conversion into mass or volume flow data
for utilization in flow control, flow monitoring, etc.
FIG. 2 shows a schematic representation of a currently used volumetric
flow meter. Note that the sampling ports 14 and 20 are positioned
in different locations along elbow 12 than those of FIG. 1. Moreover,
elbow 12 in FIG. 1 hereof is a mitered elbow 30 as opposed to the
radiused elbow 32 of FIG. 2. Pressure gauge 28 measures the pressure
difference between the two sampling ports 14 20 which may be related
to the volumetric flow in elbow 10.
When a fluid such as air flows through an elbow, pressure is lost
due to fluid friction with the walls, flow separation in the elbow,
and the setup of secondary flow (counter-rotating vortices). If
the flow through the elbow is turbulent, incompressible and steady,
the pressure differential across the elbow, .DELTA.P, is given in
terms of the dynamic pressure, .rho.U.sup.2 /2 as: ##EQU1## Here,
P.sub.1 and P.sub.2 are the static pressures upstream and downstream
of the elbow, at locations approximately as shown for the ports
in FIG. 1 hereof; .rho. is the fluid density; and U is the mean
fluid velocity at a cylindrical cross section of the elbow. The
parameter, K, is generally considered to be a function of geometry
if the flow is turbulent. For mitered elbows, the value of K is
approximately 1.1.
Elbow flow meters used in the past did not have mitered bends and
did not employ pressure ports in the locations shown in FIG. 1 hereof,
but rather were formed from radial bends and had pressure ports
as shown in FIG. 2 hereof. With the pressure ports positioned in
the bend itself, with one port on the outside and the other on the
inside thereof, the pressure measurement derives from the centrifugal
force of the fluid in the elbow. The change in linear momentum as
the fluid turns the corner in the elbow produces a pressure differential,
P.sub.3 -P.sub.4 which is: ##EQU2## where P.sub.3 and P.sub.4 are
the static pressures upstream and downstream of the elbow, at locations
approximately as shown for the ports in FIG. 2 hereof, and C.sub.k
is a flow coefficient with a value between 0.56 and 0.88. Thus,
although the form of equations (1) and (2) are the same, the force-producing
mechanisms are quite different. The difference is reflected in the
difference in value of the empirical coefficient in these equations.
For the present invention, the pressure ports are positioned such
that while the static pressure difference produced by the bend is
registered, the centrifugal force and perturbations in the region
of the bend are not registered. This typically requires positioning
the upstream port about two tube diameters upstream of the bend,
and the downstream port about four tube diameters downstream from
the bend. The exact positioning is not critical, but should be determined
in each application such that the intense turbulent effects of the
bend have had an opportunity to damp out. The use of a mitered bend
may be considered optional, but would be used if a higher pressure
drop is needed to match the requirements of a flow sensing element.
In use, the pressure drop, .DELTA.P, is measured and it is assumed
that the density and the flow coefficient are known. This allows
the velocity to be calculated from: ##EQU3## In turn, the volumetric
flow rate, Q, through the elbow meter is given by:
where A is the cross sectional area of the elbow.
Of importance to the present invention is the fact that previously,
the elbow pressure drop generator has been considered as a volumetric
flow meter based simply on measurement of the pressure difference,
not mass flow. The present invention permits an elbow pressure drop
generator to be used as a mass flow meter, which senses the mass
flow rate, m, where:
No knowledge of density is needed to obtain the mass flow rate
from a mass flow meter. However, if the density is known, then the
volumetric flow rate through a mass flow meter can be calculated
from Equation 5.
Also of importance to the present invention is that the pressure
drop across an elbow is a function of the flow coefficient and the
dynamic head (Equation 1). In general terms, for flow in the turbulent
regime, the value of the flow coefficient can be expected to be
relatively constant. Thus, once an elbow is calibrated, the relationship
between pressure drop and dynamic pressure will not change.
The use of thermal anemometers for sensing the mass flux in a flow
field is well known. A heated element such as a small cylinder is
placed in the flow. Often, heating is accomplished by applying a
voltage to either a fine wire about the element or to the semiconductor
which forms the element. When a fluid such as air at room temperature
flows across the heated wire or semiconductor, it tends to cool
the wire. Usually, the wire or semiconductor is operated at a constant
temperature, which means that additional electrical power needs
to be added to the system to maintain the temperature constant when
it is exposed to a flow field. Because there is a known relationship
between temperature and resistance for conductors and semiconductors,
the constancy of temperature can be achieved by maintaining a constancy
of electrical resistance. The system is compensated for changes
in ambient temperature which would affect the resistance of the
wire or semiconductor.
The relationship between the mass flux of the fluid and the voltage
applied to a constant temperature thermal anemometer is known as
King's law. If the flow field at the sensor location is not affected
by changes in either flow rate or fluid properties, the mass flux
is linearly related to the mass flow rate. Thus, for a given gas
(e.g., air or natural gas) and for a given geometry of the system,
the mass flow rate can be calculated by measurement of the voltage
applied to the anemometer circuit. The calculation involves use
of a calibration curve or equation.
A prototype of the elbow meter has been constructed and tested.
This version can be used over the flow rate range of 0-185 cfh (0-87
L/rain). The longest dimension of the meter is 3.2 in. (81 ram).
At a flow rate of 120 cfh (56.6 L/rain), the flow in the elbow
meter is turbulent as indicated by the Reynolds number, Re, which
has a value of approximately 8800. It can be shown that the mass
flow rate through an elbow in which the flow is turbulent can be
determined by measuring the voltage output from a laminar mass flow
shunt meter. The reading does not depend upon the density of the
fluid, but only the calibration constants of the system and the
viscosity of the fluid. Although temperature affects viscosity,
the influence upon the mass flow rate is small since viscosity changes
approximately with the square root of temperature and mass flow
rate changes with the square root of viscosity. This causes mass
flow rate to vary approximately with the fourth root of absolute
temperature. Calibration data are used to determine the values of
the coefficients of a cubic polynomial relating the mass flow rate
and powers of the voltage output.
The invention has a broad range of applications. Because it is
compact in form, it can be used to measure the mass flow rate through
scientific instruments. Also, because it has a low pressure drop
and it provides the mass flow rate rather than the volumetric flow
rate, it could be used extensively in industrial systems that involve
large flow rates. For example, in fossil fuel-fired power plants
there is a need to measure the mass flow rate of combustion air,
and the elbow meter could perform this function accurately. In the
transport of natural gas, the current technology involves the use
of orifice meters which provide data on volumetric flow rate; however,
the energy content of the fuel is dependent upon the mass, not volume,
of natural gas. Elbow meters could replace the orifice meters and
provide more appropriate and more accurate data with a lower head
loss across the meter.
The elbow mass flow meter was tested to determine if environmental
parameters (pressure, temperature and relative humidity) would have
an influence on its performance. Tests were performed by connecting
the present elbow meter in series with a calibrated rotameter whose
readings were corrected for density effects. Air was drawn through
the system by a vacuum pump and the flow rate was controlled by
a valve. The rotameter, pump, flow control valve, and the elbow
meter were placed in different chambers in which the environmental
conditions could be varied.
Calibration data from the elbow meter, when it was operated under
laboratory conditions of 24.degree. C. and 50% relative humidity,
are shown in FIG. 3. Duplicate tests were conducted at each condition.
The curve is monotonic over the standard mass flow rate range of
0 to 185 scfh (0-87 Lstd/min).
Similar curves were generated for other environmental conditions.
The data are presented in a truncated form in Table 1 where the
analog voltage from the elbow meter is given for a standard mass
flow rate of 115 scfh (54.2 L.sub.std /min.sub.). For a standard
mass flow rate range of 0 to 185 scfh, the voltage output of the
shunt is 1-5 volts. However, for the setting of 115 scfh, the coefficient
of variation of the experimental values given In Table 1 is less
than 1%. These environmental conditions cover temperatures from
-15.degree. to 39.degree. C. and relative humidities from 10 to
90%.
TABLE 1 ______________________________________ Calibration of the
Elbow Meter at Various Environmental Conditions. The standard mass
flow rate through the elbow meter was set at 115 scfh (54.2 L.sub.std
/min) and the results are given as the output voltage from the elbow
meter. Relative Output voltage, Temperature, .degree.C. Humidity,
% E, volts ______________________________________ 24 50 4.39 24
13 4.39 24 90 4.41 -15 68 4.37 1 80 4.41 39 23 4.43 ______________________________________
The system was tested at a range of simulated barometric pressures.
The elbow mass flow meter was placed inside an evacuated chamber.
Air was drawn into the elbow mass flow meter, and then passed through
a Sierra Instruments, Inc., mass flow meter which was located outside
of the chamber. The flow was then drawn through a control valve,
into a pump, and discharged to the atmosphere. Mass flow rate through
the elbow mass flow meter was determined through measurement of
the voltage output of the shunt meter and use of a calibration equation
which had the coefficients fitted from tests conducted at normal
laboratory environmental conditions. Results from these experiments
are given in Table 2 where it may be noted that for flow rates
of 1 2 and 3 cfm and for a range of pressures from approximately
21 inches of mercury to 30 inches of mercury, the mass flow rates
(in units of scfm) determined with the elbow mass flow meter were
identical to those measured with the Sierra Instruments, Inc., mass
flow meter.
TABLE 2 ______________________________________ Effect of barometric
pressure on the elbow mass flow meter. The elbow meter was operated
in series with a Sierra mass flow meter at different mass flow rates
(in units of scfm) and different values of absolute pressure. Mass
flow rate Mass flow rate Barometric from use of determined from
Pressure, inches Sierra mass use of elbow of mercury flow meter,
scfm meter, scfm ______________________________________ 29.9 3.0
3.0 25.6 3.0 3.0 21.9 3.0 3.0 29.9 2.0 2.0 26.6 2.0 2.0 24.3 2.0
2.0 21.2 2.0 2.0 29.9 1.0 1.0 26.2 1.0 1.0 24.0 1.0 1.0 21.1 1.0
1.0 ______________________________________
The configuration of the prototype elbow mass flow meter has a
nominal flow rate of 2 cfm (57 L/min) and a mitered bend. The bore
(inside diameter) of the elbow is 11/32 in. The port for shunt flow
on the upstream side of the elbow is located about two diameters
from the center of the bend while the port for the shunt flow on
the downstream side of the bend is located approximately 4 diameters
from the center of the bend. The shunt airstream flows from the
upstream port, through tubing and thence into the laminar mass flow
sensor. The flow is then rejoined with the main flow through the
elbow at the downstream port. The ports and connecting tubing are
sized such that the pressure loss across these elements is small
in comparison with the pressure loss through the laminar mass flow
sensor.
The shunt laminar mass flow sensor is attached directly to the
body of the elbow. This embodiment of the invention is used as a
mass flow meter in a commercially available instrument (Alpha Sentry,
Canberra Industries, Inc.) for measuring the alpha activity of transuranic
aerosols.
The meter can be used for either larger or smaller flow rates by
scaling the dimensions of the preferred embodiment.
The foregoing description of the invention has been presented for
purposes of illustration and description and is not intended to
be exhaustive or to limit the invention to the precise form disclosed,
and obviously many modifications and variations are possible in
light of the above teaching. For example, others skilled in the
art could conceive of shunt-type elbow meters with different configurations
such as the use of non-mitered elbows or which would have pressure
ports in other locations than those shown in the preferred embodiment.
The embodiment was chosen and described in order to best explain
the principles of the invention and its practical application to
thereby enable others skilled in the art to best utilize the invention
in various embodiments and with various modifications as are suited
to the particular use contemplated. It is intended that the scope
of the invention be defined by the claims appended hereto. |