Abstrict A traveling wave flow meter having a generally wave shaped member
which is fabricated from a flexible material and which is disposed
within a channel for conducting fluid. The flexible member undulates
in response to a flow of fluid through the channel, and the frequency
of the undulating flexible member is a function of the volumetric
flow rate of the fluid.
Claims I claim:
1. A positive displacement flow meter comprising:
(A) means for conducting fluid, having at least first and second
walls;
(B) flexure means disposed longitudinally in said conducting means
for undulating between said first and second walls of said conducting
means in response to fluid flow within said conducting means, said
flexure means having:
(1) a wavelike strip of flexible material of length X which is
forced to occupy a length L, wherein L<X,
(2) means for holding at least one end of said flexible strip,
and
(3) means for adjusting said holding means within said conducting
means;
(C) means for detecting the frequency of said flexible strip as
it undulates between said first and second walls.
2. A positive displacement flow meter comprising:
(A) means for conducting fluid, having at least first and second
walls;
(B) flexure means disposed longitudinally in said conducting means
for undulating between said first and second walls of said conducting
means in response to fluid flow within said conducting means, said
flexure means having:
(1) a wavelike strip of flexible material having a shape comprised
of at least one full wave,
(2) means for holding at least one end of said flexible strip,
and
(3) means for adjusting said holding means within said conducting
means;
(C) means for detecting the frequency of said flexible strip as
it undulates between said first and second walls.
3. An apparatus according to claim 1 or 2 wherein said holding
means includes a plurality of passages for fluid flow.
4. An apparatus according to claim 1 or 2 wherein said conducting
means includes a channel having a cover and having inlet and outlet
means.
5. An apparatus according to claim 1 or 2 wherein said frequency
detecting means comprises a reflector incorporated into said flexure
means, a light source for illuminating said reflector, and a photodetector
responsive to said reflector, disposed so that said frequency is
derived from an output signal produced by light originating from
said source that is reflected from said reflector to said photodetector
as said flexible strip undulates.
Description BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to devices for measuring flow rates, and
more specifically to a flow meter having an undulating flexible
membrane whose frequency is a function of volumetric flow.
2. Description of the Prior Art
The monolithic microprocessor has revolutionized process control
technology, but it has not yet found widespread application in practical
electrohydraulic systems. Heretofore, an obstacle to microprocessor
controlled electrohydraulic systems was the absence of an inexpensive
flow meter which would easily interface with digital logic.
One attempt to interface a flow meter with digital logic is described
in U.S. Pat. No. 4033188 issued July 5 1977 entitled "Linear
Vortex-Type Flowmeter," which discloses an electronic data
processing system for a vortex-type flowmeter wherein the fluid
to be measured is directed past a vortex-producing element to induce
fluidic variations whose frequency is a function of flow rate. These
variations are detected by a sensor yielding a signal having an
A-C component whose frequency represents the uncorrected flow rate
and a D-C component magnitude represents the temperature of the
fluid. In order to correct for the effect of temperature on the
accuracy of the reading, the signal components are separated from
each other and converted into corresponding digital values which
are fed into the data processing system to which are also applied
digital values representing the fluid characteristics, the system
producing an output signal representing the true flow rate.
The above-described system is inherently analog and requires relatively
complex electronic circuitry to interface with the digital circuitry
associated with the microprocessor. Moreover, the system is sensitive
to temperature variations which must be corrected. Accordingly,
there is a need for a more simple and less expensive flow meter
which is well adapted for digital logic interfacing.
SUMMARY OF THE INVENTION
The apparatus of the present invention provides an inexpensive
flow meter which can be easily interfaced with a microprocessor
and which is substantially insensitive to temperature variations.
The flow meter includes a strip of flexible material having a length
X which is forced to occupy a length of channel L, wherein (L<X).
As a result, the flexible material buckles and assumes a wavelike
shape inside the channel. When fluid is forced to flow through the
channel, the flexible material undulates in a traveling wave type
of displacement and the frequency of the traveling wave is a function
of the volumetric flow rate of the fluid through the channel.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a plan view of the apparatus of the present invention;
FIG. 2 is a sectional front view of the apparatus of the present
invention;
FIGS. 3A and 3B are theoretical wave shapes for the flexible member
associated with the present invention; and
FIG. 4 is a graph of the traveling wave frequency as a function
of flow rate.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring now to FIGS. 1 and 2 plan and sectional front views
of a flow meter 10 are provided. The flow meter 10 includes a housing
11 and a channel 12 which is formed therein. Preferably, the housing
11 is made of aluminum bar stock or other suitable material and
is sealed with a cover 21 which is made of plexiglass or other suitable
material. The transparent cover 21 is secured by screws 20 which
are threaded into the housing 11. The generally rectangular channel
12 is approximately 8" in length and includes an inlet 13 and
an outlet 14 through which a continuous flow of fluid may be conducted.
Disposed within the channel 12 is a flexible membrane 15 of a predetermined
length X which is forced to occupy a predetermined length L of a
portion of channel 12. The flexible member 15 is preferably fabricated
from Mylar or other suitable polymer, or it may be fabricated from
a beryllium copper compound or other suitable metal. Typically,
the flexible membrane 15 would have dimensions of approximately
0.005 inch thick, 13/16 inch wide, and 3 inches long. Moreover,
the flexible member 15 should be accurately dimensioned in width
such that there is adequate clearance for free movement of the flexible
membrane 15 inside the channel without excessive leakage flow. Forcing
the flexible membrane 15 to assume length L in a portion of channel
12 results in a buckling of the flexible membrane 15 which is hereinafter
described in greater detail.
In the preferred embodiment of the invention, the ends of the flexible
member 15 are illustrated as being held by membrane holders 16
17 through the use of clamps, epoxy or a tongue and groove type
of arrangement. The membrane holders 16 17 are slotted to allow
the passage of fluid along the flexible membrane 15. A lead screw
18 may be threaded through the housing 11 and coupled to the membrane
holder 17 such that the distance L between the membrane holders
16 17 may be precisely adjusted. A set screw 22 may be threaded
through the housing 11 to secure the membrane holder 16 within the
channel 12. It should be noted, however, that in further embodiments
of the present invention the ends of flexible membrane may be either
free or hinged. An optical detector comprised of a light source
and a photodetector is disposed within the housing 11 to detect
the displacement of the flexible membrane 15 which is either made
from a retroreflective material or includes a retroreflective strip
24 affixed to the flexible membrane 15. In further embodiments of
the invention, the optical detector 23 may be replaced by other
types of detecting devices, e.g., pressure transducers, strain gauges,
piezoelectric strain gauges, thermistors, capacitance devices, or
electromagnetic force pick-up devices. Alternatively, the flexible
membrane 15 itself could be fashioned from a piezoelectric material,
and an output signal indicative of the frequency of the flexible
membrane could be derived. In the preferred embodiment, however,
the retroreflective strip 24 causes a pulsed output signal each
time the flexible membrane 15 and the retroreflective strip pass
the optical detector 23 thereby providing an indication of the
frequency of the traveling wave associated with the undulating flexible
membrane 15.
Referring now to FIGS. 3A and 3B, theoretical wave shapes for the
flexible membrane 15 are depicted therein. The theoretical wave
shapes may be achieved through mathematical modeling. For example,
the shape of the flexible membrane 15 inside the channel 12 can
be determined by solving the differential equations that model the
buckling of beams or columns, i.e., ##EQU1## where k.sup.2 =P/EI,
P=the buckling force applied to the membrane, E=Young's modulus,
I=the moment of inertia of the membrane's cross-section, L=length,
W=displacement. The conditions which are illustrated in FIG. 3A
and which are defined by the aforementioned equation (1) are based
upon the assumptions that the deflections are small and that the
membrane follows Hook's law. A general solution that satisfies the
above-listed differential equation is given by
with the following boundary conditions: ##EQU2##
Substituting the boundary conditions (3) in the solution (2) yields
Eliminating C.sub.1 from the last two equations and simplification
yields ##EQU3## A first possible solution is provided when sin (kL/2)=0.fwdarw.(kL/2)=n.pi.
and where n=1 2 3. The buckling load becomes: ##EQU4## For n=1
the smallest buckling load becomes ##EQU5## and the shape of the
membrane becomes: ##EQU6## The constant C.sub.2 cannot be determined
but is chosen such that the membrane just touches the wall of the
channel as shown in FIG. 3a. Obviously, the solution illustrated
in FIG. 3a for the lowest buckling load is not a practical wave
shape since there will always be a leakage path through the flow
meter along the wall of channel 12 which is not in contact with
the flexible membrane 15. A second solution is provided when: ##EQU7##
The smallest root of the above equation is:
which yields a buckling load of ##EQU8## This buckling load is
larger than the smallest buckling load (n=1) associated with the
first solution but is smaller than the n=2 solution. This indicates
that if the load is gradually increased, the membrane will assume
a cosine shape from the first solution and then the membrane will
assume the shape associated with the second solution. This shape
can be obtained through eliminating C.sub.4 C.sub.3 C.sub.2 from
Equation (4) and substituting those in Equation (2) yielding ##EQU9##
Considerable simplifications will finally yield ##EQU10## The above
solution consists of the sum of a straight line and a sine wave
with a period of kL/2.pi.=0.7. Equation (6) is graphically depicted
in FIG. 3b. Equation (6) also provides a predetermination of where
the membrane touches the wall, i.e., when dw/dx vanishes, and this
occurs when x/L=0.3 and x/L=0.7. The second derivative d.sup.2 x/dx.sup.2
is proportional to a moment which may be expressed by the following
relationship: ##EQU11## Computing this second derivative, it is
found that the moment vanishes at x/L=0.15 x/L=0.5 and x/L=0.85.
The third derivative determines that the moment reaches a maximum
at x/L=0.32 and x/L=0.67. The value of this maximum moment can be
computed by substituting these values of x/L in equation (7). Accordingly,
it can be appreciated that the flexible membrane 15 can be caused
to deform in accordance with the mathematical relationships described
above when a buckling load is applied to the membrane.
When a fluid is forced through the channel 12 a wave results and
the flexible membrane 15 buckles or undulates from its initial shape
to a second shape having a 180.degree. difference in phase. During
the 180.degree. phase change a volume of fluid is displaced and
a relationship between volumetric flow rate Q and the frequency
f of the traveling wave associated with the undulating flexible
membrane 15 may also be achieved through mathematical modeling.
The fluid flows through the channel with an average velocity V.sub.ave.
Since the traveling wave flow meter is a positive displacement type
flow meter, the wave velocity equals the average fluid velocity,
and the frequency of the wave can be expressed as f=(V.sub.ave /.lambda.),
where .lambda.=wavelength, V.sub.ave =average fluid velocity, and
f=frequency of the wave. The average velocity is related to the
volumetric flow rate by the equation V.sub.ave =(Q/A), where Q=volumetric
flow rate and A=the cross-sectional area of the channel 12. Hence,
the frequency of the traveling wave can be expressed as f=(Q/A.lambda.).
In operation, therefore, the flow meter 10 utilizes the frequency
of the flexible member 15 in order to determine the volumetric flow
rate Q. Referring back to FIG. 1 it can be appreciated that a continuous
flow of fluid may be conducted into the channel 12 through the inlet
13. The incoming fluid is conducted through the slotted passages
in the membrane holder 16 and flows along the flexible membrane
15 thereby causing it to undulate. The fluid is conducted through
the slotted passages in membrane holder 17 and conducted out of
the channel 12 via the outlet 14. As the flexible member 15 undulates
between a first wave shape and a second wave shape having a 180.degree.
phase difference, the retroreflective strip 24 passes back and forth
in front of the optical detector 23 thereby providing a pulsed
output signal indicative of the frequency of the undulating flexible
member 15. The pulsed output signal can be readily applied to a
digital electronic processing means such as a counter coupled to
a microprocessor to determine the volumetric flow rate in accordance
with the algorithms described above.
Referring now to FIG. 4 a graphic representation of the frequency
of the flexible membrane 15 is plotted as a function of the flow
rate of oil through the flow meter 10. In experiments, the oil flow
rate was varied from zero to approximately 2.5 gpm at a temperature
of 100.degree. F. and 140.degree. F., and the frequency of the traveling
wave was measured. It can be appreciated that experimental results
conformed well to theoretical expectations. Moreover, it should
be noted that the positive displacement nature of the traveling
wave flow meter 10 suggests that it is substantially insensitive
to temperature variations in the flowing fluids.
While the invention has been described in its preferred embodiments,
it is to be understood that the words which have been used are words
of description rather than limitation and that changes may be made
within the purview of the appended claims without departing from
the true scope and spirit of the invention in its broader aspects. |