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1206 IEEE SENSORS JOURNAL, VOL. 7, NO. 8, AUGUST 2007
A Low-Cost Centrifugal Force Type Flow Sensorfor Measuring the Flow Rate of a Fluid
Through a PipelineSatish Chandra Bera
Abstract—In this paper, attempts have been made to develop avery simple low-cost flow sensor by using the effect of centrifugalforce of a fluid on circular pipe section. The theoretical analysisof the sensor is reported in this paper. The centrifugal force de-veloped by the flowing fluid on one end of a common balance hasbeen sensed by an inductive pickup placed in a bridge network.The output of the bridge network has been found to vary with flowrate. Experiments have been carried out to find the static charac-teristic of the sensor and the experimental results are reported inthis paper. From these experiments, it has been observed that theexperimental graph follows the theoretically predicted character-istic with very good repeatability.
Index Terms—Bridge network, centrifugal force, common bal-ance, flow rate measurement, inductive pickup, pipeline.
I. INTRODUCTION
THE ACCURATE measurement of flow of a fluid through apipeline is one of the most important requirements in any
process plant in order to run the plant with optimum efficiencyat lesser cost. There are various effects like the effect of energyassociated with a flowing fluid through a pipeline, Doppler ef-fect, and the effect of speed of the fluid suction pump on theflow rate, etc., which have been utilized in designing the var-ious flowmeters [2]–[5]. In the coriolis flowmeter [2], [5], theeffects of the velocity of a flowing fluid and the velocity of vi-bration of a pipeline section through which the fluid flows areutilized to produce a coriolis force which acts on the pipe wall inthe opposite directions in the upstream and downstream sides.As a result, with respect to the center of the pipeline section,the resultant oscillation of the upstream side will lag and that ofthe downstream side will lead. The delay in time between thevibrations of these two sides is directly proportional to the massflow rate [2], [7]. Hence, this measurement is very accurate. Var-ious works on the effect of various factors like properties offluid, operating conditions, and installation technique, etc., oncoriolis mass flowmeters have been reported. Storm et al. [6]have proposed a model-based correction of the coriolis massflowmeter and Cheesewright et al. [8] have identified differentexternal factors on the performance of coriolis mass flowmeters.In anemometer type mass flowmeters [1], [4], [5], the cooling
Manuscript received November 2, 2006; revised December 23, 2006; ac-cepted February 26, 2007. The associate editor coordinating the review of thispaper and approving it for publication was Prof. Gerald Gerlach.
The author is with the Instrumentation Engineering Section, Department ofApplied Physics, University of Calcutta, Kolkata-700009, West Bengal, India(e-mail: [email protected]; [email protected]).
Digital Object Identifier 10.1109/JSEN.2007.897963
effect of a flowing fluid on a heating element inside the fluidis utilized in terms of change in resistance of the element withflow rate. In the vortex flowmeter [2]–[5], frequency of vorticesproduced behind a blunt post in a pipeline under turbulent con-ditions is directly proportional to the volume flow rate of thefluid passing through the pipeline. Rodgers et al. [9] have de-veloped a flow sensor module consisting of an application-spe-cific-integrated-circuit (ASIC) with a fluidic oscillation elementand a differential capacitive pressure sensor (SCS) mounted ina sealed aluminum casing. Svedin et al. [10] have developed amicromachined silicon torque sensor which senses the torqueproduced at the bearing surface of the static turbine placed in aflow tube and has shown that this torque is linearly related withthe volume flow rate through the pipeline.
In this paper, a new type of flow sensor has been proposed.This sensor consists of a vertical semicircular pipeline sectionconnected with the main pipeline through metallic or non-metallic bellows junctions in such a way that when a fluid flowsthrough the semicircular pipeline section, the effective cen-trifugal force produced by the circular motion of the fluid actsin the vertically downward direction. This force is utilized toproduce the displacement of the soft iron core of the inductivepickup coil placed in a Maxwell’s bridge circuit. The pipelinesection is vertically placed on the weighing pan at one end ofthe beam of a common balance and an identical semicircularsection are placed on the other pan at the other end of the beamso that the beam is horizontal when there is a no flow of thefluid and the effect of static pressure is eliminated. The verticalcore of the inductive pickup coil is rigidly attached with thatend of the common balance carrying the flow sensing section.The centrifugal force of the fluid produces a small displacementof this core. Therefore, the inductance of the pickup coil andthe output of the bridge network changes with the change offlow. A definite parabolic relation between this bridge outputand volume flow rate has been mathematically derived. Exper-iments have been performed to measure the bridge output atdifferent flow rates of the fluid. The experimentally observedcurve is found to follow the theoretically derived equation. Thetheoretical deduction and experimental data are presented inthis paper.
II. METHOD OF APPROACH
Let us consider a fluid of density “ ” flowing with a velocity“ ” through a semicircular cylindrical pipe of radius “ ” andcross section “A” placed in a vertical plane, as shown in Fig. 1.
Let us consider an elementary length of the circularpipe at an angle from the horizontal axis, as shown in Fig. 1.
1530-437X/$25.00 © 2007 IEEE
BERA: A LOW-COST CENTRIFUGAL FORCE TYPE FLOW SENSOR FOR MEASURING THE FLOW RATE OF A FLUID THROUGH A PIPELINE 1207
Fig. 1. Semicircular pipeline section.
The centrifugal force by this element acting radially outwardsis given by
(1)
Hence, vertically downward component of this force alongaxis is given by
or (2)
and the horizontal component is given by
(3)
Hence, the effective horizontal component of the centrifugalforce is given by
(4)
i.e., there will be no effective horizontal component of the cen-trifugal force.
The effective vertically downward component of the cen-trifugal force is given by
(5)
Therefore, in terms of the volume flow rate , the aboveequation is reduced to
(6)
In order to measure this force and reduce the effect of turbu-lence, the two ends of the above semicircular pipeline sectionare extended in the form of the straight long vertical pipelinesections so that the sensor takes the form of a vertical U-tubesection, as shown in Fig. 2. This U-tube is connected with themain pipeline through metallic or nonmetallic bellows junctionsand rests on the pan at one end of the beam of a common bal-ance, as shown in Fig. 2. A similar U-tube section with bellowsjunctions is placed on the other end of the beam in order tocounteract the effect of static pressure, as shown in Fig. 2. Thissecond U-tube senses and compensates the effect of static pres-sure since it is connected with the flow tube only at one junction.At no flow condition of the fluid, the beam is made horizontal byplacing fixed dead weights on either end of the beam if needed.The end of the beam carrying the flow sensing U-tube sectionis rigidly attached with the soft iron core of an inductive pickupcoil, as shown in Fig. 2.
Fig. 2. Centrifugal force type flow transducer.
Fig. 3. Maxwell’s bridge circuit for sensing the displacement of the flowsensing U-tube section.
When the liquid flows through this U-tube section via the bel-lows junction, the upper straight part of the U-tube reduces theeffect of turbulence of the liquid and the lower semicircular partsenses the centrifugal force produced by the fluid. So when thefluid flows, the end of the beam of the common balance carryingthe sensor U-tube section moves downwards along with the coreof the inductive pickup coil by the action of centrifugal force, asshown in (6). The pickup coil consists of two parallel magneticpaths which decreases the effective reluctance and, hence, in-creases the sensitivity of the coil. This pickup coil is connectedin one of the ratio arms of a Maxwell’s bridge circuit, as shownin Fig. 3, whereas the other ratio arms consists of the identicaldummy inductance coil so that at no flow condition of the fluid,the bridge is almost at balanced condition when the resistancesin the other ratio arms are identical.
From the construction of the pickup coil, as shown in Fig. 2,it is found that the coil along with its movable core has twoparallel magnetic reluctance paths like a shell type transformer.The effective reluctance “ ” of this magnetic circuit is given by
(7)
where permeability of the movablecore material, permeability of iron frame mate-
1208 IEEE SENSORS JOURNAL, VOL. 7, NO. 8, AUGUST 2007
rial, area of the movable core,area of the magnetic path in the frame material,length of the magnetic path in the frame at one side,of the small air gap between the core and the frame,of the core at no flow condition inside the pickup coil, and
of the core or U-tube due to the centrifugalforce produced by the flow.
Hence, at fluid flow rate “ ,” the effective magnetic reluc-tance of the coil can be written as
(8)
where and are constants given by
(9)
and
(10)
So, the inductance of the pickup coil is given by
(11)
where is the number of turns of the coil.Since , so from (9) and (10), . Hence,
the above equation is reduced to
or
(12)
where is the inductance of the pickup coil atno flow condition and is the change ininductance of this coil due to the fluid flow through the pipeline.From Fig. 3, the bridge output voltage for sinusoidal supplyvoltage is given by
(13)
Now, the bridge is balanced at no flow condition when the beamof the common balance is horizontal so that .Hence, putting this condition in the above equation, the bridgeoutput at flow condition of the fluid is given by
(14)
Since , the above equation is reduced to
or
(15)
Now, the displacement of the core is due to the centrifugalforce only. Since the beam of the balance is initially madehorizontal at no flow condition of the fluid and the centrifugal
Fig. 4. Experimental setup for testing the proposed flow sensor.
force due to the flowing fluid is generally small, so the displace-ment of the core may assumed to be directly proportional tothe centrifugal force .
Hence
or (16)
where is the constant of proportionality. Combining (6),(15), and (16), we get
(17)
Hence, for a given fluid, the bridge output will have almost aparabolic relation with the fluid flow rate ( ).
III. EXPERIMENT
The proposed flow sensor has been designed and fabricatedby using a common balance and two exactly identical U-tubeflow sections made of 0.5 inch or 12-mm diameter PVC tube.The lower semicircular part of each U-tube is selected to havea mean diameter of about 100 mm and length of the verticalstraight part of the U-tube is selected to be about 250 mm. TheseU-tubes are connected with the main 1 inch diameter watertube through metallic bellows elements, as shown in Fig. 2. TheU-tubes are placed vertically on the weighing pans of the beamof a common balance and suitable dead weights are placed sothat the beam is horizontal when there is no flow through theU-tube and they are filled with the water at rest. Under this con-dition, the soft iron core attached with the sensing U-tube end ofthe beam takes a particular position inside the inductive pickupcoil up to a length , as shown in Fig. 2. Now, values of the re-sistances and in the ratio arm of the Maxwell’s bridge areadjusted until the bridge output is minimum. The bridge outputvoltage is measured by using a 4 1/2 digit multimeter and a CROas the detector. The experimental setup is shown in Fig. 4
In this experimental setup, an overhead water tank is main-tained at a constant level by ensuring its inlet flow rate greaterthan the exhaust flow rate. The water from this tank is allowedto flow in the U-tube flow sensor through a manually operatedvalve. The flow through this U-tube is changed in steps bya manually operated valve connected in the pipeline in bothincreasing and decreasing modes and at each step, the bridgeoutput is measured. The flow rate is measured by direct water
BERA: A LOW-COST CENTRIFUGAL FORCE TYPE FLOW SENSOR FOR MEASURING THE FLOW RATE OF A FLUID THROUGH A PIPELINE 1209
Fig. 5. Characteristic graph of the proposed flow sensor.
Fig. 6. Percentage deviation from the best-fit static characteristic of the flowsensor.
collection method. The identical repeatable results were ob-tained. The bridge output voltage is then plotted against flowand a parabolic static characteristic graph has been obtained, asshown in Fig. 5. The percentage deviation of the experimentaldata from the best-fit parabolic characteristic has been calcu-lated and is shown in Fig. 6.
IV. DISCUSSIONS
From Fig. 5, it is found that the static characteristic graphof the proposed flow sensor has a parabolic nature which al-most follows the characteristic (17). During the increasing anddecreasing modes of experiment, the identical results were ob-tained for the same flow rate. This shows a very good repeata-bility of the flow sensor. The nonlinear characteristic graph canbe easily linearized by using microprocessor [11] or PC-based[12] linearization technique. The construction of the transduceris very simple and the measurement involves no contact of theprocess fluid. Hence, the transducer may be regarded as a verylow-cost unit in comparison with the existing flowmeters likecoriolis flowmeter and vortex flowmeter, etc. The only defect ofthe instrument is the use of a bellows element junction whichmay be damaged at very high pressure but a suitable selectionof the bellows material can eliminate this defect. The use ofcommon balance tends to affect the compactness of the instru-ment. This may be eliminated by using a compact lever systemrigidly fixed in a flow tube.
From (6) it follows that the sensitivity of the sensor increaseswith the decrease of the cross sectional area (A) of the sensingpipe. Hence to measure flow rate in a large diameter pipeline,the flow sensor of a very small cross section may be used in abypass line of the main pipeline and a correction factor may beused for the flow rate measurement in a large pipeline.
The preliminary results of the experimental analysis of theproposed transducer are reported in this paper. The work on themanufacture of prototype industrial units of the sensor and theirtesting are now in progress considering all the above points.Some preliminary encouraging results have been obtained withvery good repeatability and reliability by using a compact leverarrangement rigidly fixed in the flow head box with micro-controller-based head mounted linearizer and transmitter. Thecharacteristic of the transducer may depend on the flow tubecross-sectional area or Reynolds number. After manufacturinga number of units of different diameters, this will be studied.
Moreover, the results reported in this paper may be assumedto be reliable due to the fact that the flow rate has been measuredby the direct water collection method for five to six observationsat constant static head pressure for each reading with the exper-imental setup, as shown in Fig. 4. Hence, the comparison withother flowmeters may not arise as the static parameters of thetransducer are easily realized from the static characteristic graphshown in Fig. 5. A comparative study of the dynamic character-istic of the transducer with other flowmeters is in progress nowand will be reported later.
The points of contact of the U-tube sections with theweighing beams of the common balance were made rigid inorder to avoid the effects of vibration during fluid flow. Theflow sensor was mounted in a location so that the U-tubesare kept vertical and are always filled with fluid. The distancebetween the two U-tube sections was made small in order toreduce the effect of line pressure drop on flow sensor output.
REFERENCES
[1] S. Oda, M. Anzai, S. Uematsu, and K. Watanabe, “A silicon microma-chined flow sensor using thermopiles for heat transfer measurements,”IEEE Trans. Instrum. Measure., vol. 52, no. 4, pp. 1155–1159 , Aug.2003.
[2] R. C. Baker, Flow Measurement Handbook: Industrial Designs, Oper-ating Principles, Performance and Applications. Cambridge, U.K.:Cambridge Univ. Press, 2000.
[3] Bela and G. Liptak, Process Measurement and Analysis, 3rd ed.London, U.K.: Butterworth, 1999.
[4] J. P. Bentley, Principles of Measurement Systems, 3rd ed. Singapore:Longman Singapore Publishers (pte) Ltd., 1995.
[5] E. O. Doeblin, Measurement System Application and Design, 4th ed.New York: McGraw-Hill, 1990.
[6] R. Storm, K. Kolahi, and H. Rock, “Model-based correction of coriolismass flowmeters,” IEEE Trans. Instrum. Measure., vol. 51, no. 4, pp.605–610, Aug. 2002.
[7] K. Kolahi, T. Cast, and H. Rock, “Coriolis mass flow measurement ofgas under normal conditions,” IEEE Trans. Instrum. Measure., vol. 5,no. 4, pp. 275–283, 1994.
[8] R. Cheesewright, C. Clark, and D. Bisset, “The identification of ex-ternal factors which influence the calibration of coriolis mass flow me-ters,” J. Flow Meas. Instrum., vol. 11, no. 1, pp. 1–10, Mar. 2000.
[9] B. Rodgers, S. Goenawan, M. Yunus, Y. Kaneko, and J. Yoshiiken, “A16- A interface circuit for a capacitive flow sensor,” IEEE J. Solid-StateCircuits, vol. 33, no. 12, pp. 2121–2133, Dec. 1998.
[10] N. Svedin, E. Stemme, and G. Stemme, “A static turbine flow meterwith a micromachined silicon torque sensor,” J. Microelectromechan.Syst., vol. 12, no. 6, pp. 937–946, Dec. 2003.
1210 IEEE SENSORS JOURNAL, VOL. 7, NO. 8, AUGUST 2007
[11] J. K. Roy, K. Naskar, and S. C. Bera, “A low cost microprocessor basedliquid level transmitter using inductive pick-up,” J. Instn. Engs. (I), vol.80, pp. 17–22, 1999.
[12] S. C. Bera, J. K. Ray, B. Chakraborty, D. N. Koley, and M. N. Mandal,“A PC based linearisation technique of a hall probe type level trans-ducer,” in Proc. Inst. Elect. Eng. Int. Conf. Energy, Inf. Technol. PowerSector, Kolkata, Jan. 28–29, 2005, PEITSICON-2005.
Satish Chandra Bera was born in West Bengal,India, in 1952. He received the B.Tech., M.Tech., andPh.D. (Tech.) degrees in instrumentation engineeringfrom the University of Calcutta, Calcutta, India, in1976, 1978, and 1988, respectively.
He worked as an Instrumentation Engineer withHindusthan Fertilizer Corporation Ltd., India, fornine years and then joined the University of Calcuttaas a member of the faculty in 1991. Presently, he hasbeen working as a Reader in Instrumentation Engi-neering at the University of Calcutta and is involved
in carrying out a number of research projects on transducer development,process plant instrumentation, process modeling, biomedical instrumentation,etc., leading to Ph.D. degrees for a number of scholars. He has received anumber of patents on transducers.
