Measuring and testing – Volume or rate of flow – By measuring electrical or magnetic properties
Reexamination Certificate
2001-02-14
2003-11-25
Lefkowitz, Edward (Department: 2855)
Measuring and testing
Volume or rate of flow
By measuring electrical or magnetic properties
Reexamination Certificate
active
06651511
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates generally to fluid flow measurement methods and apparatus, and more particularly to a new method and apparatus for measuring the mass flow rate of fluids flowing through closed conduits using the Magnus Effect. In accordance with the invention, an oscillating probe is extended into a flow stream and experiences an oscillating Magnus “lift force” that relates to fluid mass flow rate.
BACKGROUND OF THE INVENTION
Historically, the Magnus Effect and its more rigorous counterpart, the Kutta-Joukowski Theorem (“KJT”), have been used to describe the lift force experienced by a spinning cylinder immersed in a transversely flowing air stream. The KJT mathematically describes the phenomenon of lift resulting from fluid flowing around the object. Using the KJT, one can demonstrate that if an object such as a cylinder (sphere or other shaped object)
10
is placed in an air stream
12
, as depicted in
FIG. 1
, no lift force results. However, rotating the cylinder
10
about its axis
13
as suggested by the arrow
14
, and in the flowing stream
12
produces a lift force F
L
. The lift force experienced by the rotating cylinder is called the “Magnus Effect” in recognition of Heinrich Magnus, a German Physicist, who studied deviations in the trajectories of spinning artillery shells. It is now understood that the Magnus lift force explains why baseballs “curve”, tennis balls “cut”, and golf balls “hook” or “slice”. The KJT describes the lift force F
L
acting on a cylinder of length L, radius R, spinning at a rate of S revolutions per unit time about its longitudinal axis
13
as proportional, in part, to the product of fluid density and fluid velocity. According to the KJT, the lift force per unit length, F
L
, exerted on the spinning cylinder is:
F
L
=&rgr;V&Ggr;
(1)
Where &rgr;=air density, V=free stream air velocity, and &Ggr;=the circulation of fluid around the object defined as the line-integral of the fluid velocity around the spinning cylinder's circumference C:
&Ggr;=∫
C
V
R
dr=
2&pgr;
RV
R
(2)
V
R
is the fluid velocity at the periphery of the cylinder and, in this particular case, equals the cylinder's peripheral surface velocity because the fluid boundary layer adheres to the cylinder's surface. V
R
=2&pgr;RS, is the velocity of the rotating cylinder at its periphery with S being the rate at which the cylinder spins. The direction of the lift force is perpendicular to both the cylinder's longitudinal axis and the direction of the fluid velocity V as depicted in FIG.
1
. The Magnus lift force is distributed along the portion of the cylinder's length exposed to the fluid stream. Equation (1) applies to a surface of any cross-sectional shape regardless of whether the circulation, &Ggr;, is “mechanically induced” (as with rotating a cylinder), “natural” (as with an airfoil), or a combination thereof.
Classically, the Magnus Effect applies only to mechanically induced circulation of fluid around an object (but not necessarily cylindrical in shape). Mechanically induced circulation causes the boundary layer adhering to the cylinder's surface to interact with the flowing stream resulting in a momentum transfer from the free-stream flow, across the boundary layer, to the cylinder. This momentum transfer causes the rotating object to experience a lift force directly proportional to the momentum of the fluid stream. The mass flow rate, Q
M
, of a fluid of density, &rgr;, flowing with average velocity, V, through a conduit of cross sectional area, A
c
, is:
Q
M
=&rgr;VA
c
(3)
The ability to measure a fluid's rate of mass flow using the Magnus Effect is based partially on the fact that, the magnitude of the Magnus lift force, like the fluid mass flow rate, Q
M
, is proportional to &rgr;V.
Others in the field have recognized the potential applicability of this technique to the measurement of mass flow rate. For example, in the Japanese Application Number JP1990000128718 of OGAWA YUTAKA and KAWAOTO HIROSHI with Issued/Filed Dates of Jan. 27, 1992/May 17, 1990, the applicants disclose that they believe they can measure mass flow rate by using a strain gage to determine the Magnus dynamic lift on a cylinder rotating at constant speed in a viscous fluid. The Magnus dynamic “lift” is measured as a function of the change of the strain of strain gages, and the change in the strain quantity is converted to an electrical signal by a bridge circuit to provide a value proportional to the geometric product of the flow velocity and the density. This information is then used to determine mass flow rate.
In a second Japanese Application Number JP1992000101875, bearing Issued/Filed Dates of Oct. 22, 1993/Mar. 29, 1992, to INA YOSHITAKA, NAKAO SHINICHI and HAYAKAWA MASAO, the mass flow rate of a gas flow running at a fixed velocity V through a passage is measured by a rotary cylinder disposed in the gas passage and rotated at a fixed peripheral velocity. Pressures P
1
and P
2
generated on opposite sides of the outer periphery of the rotary cylinder by this rotation are supplied to a differential pressure detector and the differential pressure between the sensors is determined. Based on this differential pressure, the mass flow rate Q
m
is determined using the relationship of P=2Q
m
(v/A).
Both of these references require that rotation of the cylinder be kept constant; that is, they require rotating a drive motor at constant rotating speed. The second reference also requires that pressures P
1
and P
2
generated in the vicinity of the “upper and lower places” of the outer periphery of the rotary cylinder be measured to determine mass flow rate. These approaches have certain disadvantages. For example, the need to rotate the cylinder at constant speed requires closed-loop feedback and control of motor speed, which adds expense. Not having adequate motor speed control is a serious limitation, in that any variation in motor speed will directly result in a mass flow measurement error.
Another disadvantage is that these approaches require sealing of the “cylinder”, or its connecting shaft, from the fluid, and from the cylinder's drive motor and the “outside world”. This type of construction imposes multiple problems that affect performance, reliability, and usage/application. Sliding seals or gaskets exhibit a pressure sensitivity that can exert forces on the probe, which can compete with the Magnus force, thereby producing mass flow measurement errors. This is especially important in that many industrial applications experience flow pulsation due to fans, compressors, and pumps. Sliding seals can also present fluid compatibility problems with highly corrosive fluids, and/or safety problems related to the reliable sealing or escapement of toxic or volatile fluids. Also, seals require maintenance, and impose pressure-rating limitations. Sliding seals also exert friction on motor parts that can influence motor speed control. Because seals must by their nature be compliant, they necessarily “absorb” some of the cylinder's Magnus force deflection and thereby further limit the ability of the apparatus to measure lower mass flow rates accurately, particularly in the case of gases.
A further disadvantage is that strain gauges have limited usefulness because they must be bonded securely and permanently to the cylinder shaft. The integrity of the bond can degrade with temperature, thereby restricting the useful operating temperature range. Moreover, pulsations and vibrations coupling into the cylinder from the pipe and fluid can introduce periodic and random signals into the strain gauges that can be misinterpreted as being “real” and related to mass flow.
Still another problem associated with the Japanese inventors' approaches is that they require pressure sensing. This can restrict the useful measurement range at low differential pressures. It also adds cost and more complexity to the device. Pressure se
Burns Doane , Swecker, Mathis LLP
Hamrick Claude A.S.
Lefkowitz Edward
Mack Corey D.
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