Measuring and testing – Volume or rate of flow – Using differential pressure
Reexamination Certificate
1999-08-30
2002-03-05
Fuller, Benjamin R. (Department: 2855)
Measuring and testing
Volume or rate of flow
Using differential pressure
Reexamination Certificate
active
06352001
ABSTRACT:
BACKGROUND OF THE INVENTION
This invention relates to the determination of mass flow rate and, more particularly, to an accurate, non-iterative method of calculating mass flow rate using a pressure differential device, such as a venturi flow meter. In an exemplary application, this non-iterative method can be implemented within the controller of a combined-cycle power generation system for computing steam flow rate for each venturi in the steam cooling system.
The steam cooling system for a combined cycle plant incorporates multiple venturis for steam flow rate control and protection. These venturis must provide accurate flow rate information over a range of steam pressures and temperatures to ensure successful operation of the system.
With reference to
FIG. 1
, a venturi
10
is a pressure differential device which is inserted in a conduit and is used to determine the rate of flowing fluid within the conduit. In
FIG. 1
a conduit
12
is illustrated having a longitudinal flow path through which a fluid may flow as shown by the flow arrow. The upstream pressure P
1
is sensed by a fluid pressure sensor
14
. A temperature probe
16
is provided to detect fluid temperature upstream. Pressure P
2
is detected in the throat
18
of the venturi. A flow computer or processor
20
receives pressure P
1
, pressure P
2
and the temperature T. Based on this information and predetermined information, the processor calculates the flow rate. The measurements are shown referenced to upstream conditions only as an example.
Discharge coefficient is a variable in the computation of venturi mass flow rate. Reynolds number is a measure of the ratio of the inertial to viscous forces that the flowing fluid experiences within the venturi. A flow calibration performed on the venturi will reveal how the discharge coefficient varies with Reynolds number. A typical plot of flow calibration data is illustrated in FIG.
2
. Note that the discharge coefficient drops off quite rapidly for low Reynolds numbers.
The current approach to obtaining venturi mass flow rate involves either an iteration upon mass flow rate or an assumption of constant discharge coefficient.
In accordance with the iteration method, since both discharge coefficient and Reynolds number are a function of mass flow rate, which is unknown, a guess is first made at the discharge coefficient. From this discharge coefficient, a mass flow rate, q
m
, is computed as follows, using the ASME definition of venturi mass flow rate, See e.g., “Measurement of Fluid Flow in Pipes Using Orifice, Nozzle, and Venturi,” ASME MFC-3M-1989:
q
m
=0.09970190
CY
1
d
2
(
h
w
&rgr;
fl
/(1−&bgr;
4
))
0.5
(1)
wherein:
q
m
=mass rate of flow, lbm/sec
C=venturi discharge coefficient, dimensionless
Y
1
=expansion factor based on upstream absolute static pressure, dimensionless
d=venturi throat diameter at flowing conditions, inch
D=upstream internal pipe diameter at flowing conditions, inch
h
w
=differential pressure, inches of water
&rgr;
fl
=density of the flowing fluid based on upstream absolute static conditions, lbm/cuft
&bgr;=diameter ratio at flowing conditions, &bgr;=d/D, dimensionless
Reynolds number, R
d
is then computed from mass flow rate as follows:
R
d
=48
q
m
/(&pgr;
d
&mgr;) (2)
wherein:
R
d
=Reynolds number referred to d, dimensionless
q
m
=mass rate of flow, lbm/sec
d=venturi throat diameter at flowing conditions, inch
&mgr;=absolute viscosity of the flowing fluid, lbm/ft-sec, based on upstream temperature.
In the same reference (ASME MFC-3M-1989), an equivalent expression for mass flow rate based on downstream conditions (pressure and temperature) is given.
Since the venturi flow calibration is typically presented as a curve relating discharge coefficient to Reynolds number (see, for example, the typical calibration curve of FIG.
2
), a new discharge coefficient can then be computed from the Reynolds number. From this new discharge coefficient, a new mass flow rate is then computed using Equation 1. This process is repeated until the change in computed mass flow rate from one iteration to the next is insignificant.
In accordance with the constant discharge coefficient method, discharge coefficient is assumed to be constant, which eliminates the need to iterate. However, this method limits the ability to accurately compute mass flow rate, especially in the low Reynolds number region where the discharge coefficient can vary quite dramatically.
BRIEF SUMMARY OF THE INVENTION
A non-iterative method for obtaining mass flow rate using a pressure differential flow meter is provided by the invention. More specifically, a non-iterative routine has been developed to compute mass flow rate quickly and accurately by incorporating the results from a flow calibration performed on each venturi directly in the computation.
Accordingly, the invention is embodied in a method for determining mass flow rate of a fluid flowing through a conduit having a first flow passage area, comprising the steps of: providing a pressure differential device comprising a flow constriction defining a fluid passage having a second flow passage area; flowing fluid through the pressure differential device; sensing a fluid pressure P
1
at a first pressure sensing location in the conduit remote from the flow constriction; sensing a fluid pressure P
2
at a second pressure sensing location downstream of an entrance of the flow constriction; and determining the mass flow rate based on sensed values of the fluid pressure P
1
and the fluid pressure P
2
, and an expression of discharge coefficient C as a function of Reynolds Number R
d
determined from flow calibration data obtained by performing a flow calibration on the flow constricting member. In the presently preferred embodiment, the functional expression is a polynomial expression, and the mass flow rate is determined based on the polynomial coefficients of the polynomial expression. In the presently preferred embodiment, furthermore, a fluid temperature T in the conduit is also sensed and the sensed temperature is used in the determination of mass flow rate.
REFERENCES:
patent: 3686946 (1972-08-01), Halmi
patent: 3733901 (1973-05-01), Halmi
patent: 4396299 (1983-08-01), Clingman, Jr. et al.
patent: 4528847 (1985-07-01), Halmi
patent: 6012474 (1985-07-01), Takamoto et al.
patent: 5226728 (1993-07-01), Vander Heyden
patent: 5323657 (1994-06-01), Vander Heyden
patent: 5365795 (1994-11-01), Brower, Jr.
patent: 5682410 (1997-10-01), McGrady et al.
patent: 5880378 (1999-03-01), Behring, II
The American Society of Mechanical Engineers; Measurement of Fluid Flow in Pipes Using Orifice, Nloozzle and Venturi; 1990; p 10.
Box et al; “Statistics for Experiments: An Introduction to Design, Data Analysis, and Model Building”; 1978; pp 482-483.
Rajamani Ravi
Wickert Thomas Edward
Fuller Benjamin R.
General Electric Company
Nixon & Vanderhye PC
Thompson Jewel
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