Sensors and Actuators A, 37-38 (1993) 403-409
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Development of an ultrasonic transducer using long acoustic waves for flow measurement E S Ikpe, G G Scarrott, J P Weight and K T V Grattan Measurement & Instrumentatzon Centre, School of Engzneerzng, Czty Unzverszty,Northampton Square, London EC1 V OHB (UK)
Abstract The ultrasonic technique for flmd-flow measurement m a pipe mvolves measurmg the small change m the net velocity of sound waves m the flmd due to Its motion A well-established technique for this uses sound of very short wavelength generated by transducers wth lateral dnnenslons large compared with the wavelength, so that the wave 1spropagated as a beam directed diagonally acros the pipe This technique IS widely used for pipes larger than about 100 mm m diameter, but ISunsatisfactory for smaller prpes, smce the practicable acoustic path length ISproportional to the pipe diameter To meet the requvement for accurate flow measurements m smaller (less than 100 mm. diameter) pipes, a transducer has been developed usmg a wavelength m the flmd such that the pope serves to guide the wave and, m effect, to make the acoustic path length longer than the pipe diameter The design of the transducer IS reported and results obtained on lta performance point to sunple flow-meter designs that are flexible m application and measure the mean velocity over the pipe cross se&on, regardless of whether the Row IS lammar or turbulent
Introduchon In sonic flow meters [l] whose operation 1s based on transit-tune methods (of some waves m a fluid), the flow velocity 1s often inferred from one of three systems which determme the drect transverse time, phase or frequency difference of acoustic waves that have traversed the flow path between the sendmg and recelvmg transducers The waves are often propagated m the form of beams at a certain angle of mcldence to the flow ax+ and nnpose severe hmltatlons on the accuracy of flow meters, especially for flow lines using smalldiameter pipes These include a limited acoustic path length, samphng of flow only along the sound path, and extraneous signals ansmg from side lobes of the beams and from higher-order modes m the pipe Reflections from these side lobes and from higher-order tube modes are temperature and flow-profile dependent, m a manner that is difficult to predict Consequently, a flow meter based on the propagation of such beams 1s expected to dnft m value The velocity of pressure waves m a fluid (typically up to 1 3 x lo6 mm s-‘) 1s much greater than the flmd flow velocity of practical mterest (typically 10’ mm s-l), so that to achieve a precrsion of-even 1% it IS necessary to measure the tnne delay of the sound wave to a preaslon of better than 1 part m lo5 The use of waves that are guided by the pipe can help to increase the acoustic path length, prevent the generation of unwanted pipe modes due to reflectlons, allow for the mterrogatlon of the flow path over the cross
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section of the pipe and, m effect, improve the accuracy of transit-tune ultrasomc flow meters These pomts are expounded m several pubhcatlons, for example, refs l-4
A wave m a fluid IS guided by the pipe containing it If the wavelength m the fluid 1sat least twice the dmmeter of the pipe In very large pipes, the generation and detection of long waves have been affected by a loudspeaker-rmcrophone arrangement [ 51 This approach 1s unsuitable as the dimensions of the pipe reduce, espenally for pipes vvlth a diameter m the range 5- 100 mm In this paper the development of a novel transducer for use m generating and detecting long waves m a flmd m a pipe wlthm the size range stated above 1s reported, as a means for effective flow measurements using a flow cell wth known and controllable standmg-wave patterns
Transducer principle and design The basic element of the long-wave transducer developed m this work 1s a short length of the pipe, contammg or transportmg the flmd whose volume flow rate 1s to be measured, and made to resonate at the frequency that would permit the pipe to gmde the ensumg waves The natural radial resonance frequency of a cyhndncal pipe is m inverse propotion to its diameter For example, for small copper pipes of diameter m the range 5-100 mm, the radml or rmg frequency is m the range 255- 13 kHz A workmg copper pipe size of
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Elsewer Sequoia All nghts reserved
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22 mm was chosen, wth water as the fluid to be transported In tlus case, the rmg frequency 1s about 60 kHz, which m water at room temperature produces a sound wavelength of about 26 mm This 1s comparable urlth the pipe diameter and renders the wave ungmded by the pipe A guided wave 1s produced when the radial frequency of the vlbratmg section of the pipe can be lowered to about 23 kHz A workmg frequency of 17 kHz was chosen to make the sound wavelength m water about four times (or less) the diameter of the pipe To achieve this expenmentally, a circular flat of the nght thickness was pressed on the resonating pipe section to sunulate a vibrating cucular disc, which 1s edge-clamped according to the mathematical model [6]
wmdmg, so that the combmatlon of the wmdmg, the magnetic core, and the pipe flat constitutes a transformer The cn-culatmg current m the flattened regon of the pipe interacts with the polarlnng magnetic field to generate an alternating force that imparts a lateral vibration to the resonant flat Thus the flat serves three purposes, m addition to its obvious function of contammg the fluld as part of the pipe It acts as the s&e-turn low-impedance winding of a transformer, a one-turn moving co11 m a magnetic field, and as the resonant element The resulting device IS, m effect, a transformercoupled movmg-co11 transducer that obviously operates equally as a transnutter or detector of pressure waves m the fled at the resonance frequency of the flattened pipe
Fabrication details
wheref, 1s the fundamental-mode mechanical resonance frequency of the flat, /I,, is a constant which equals 1 88 for this mode, ubar 1s the sound velocity m a bar of the matenal, which for copper IS x3813 m s-‘, 0 1s the Poisson ratlo and IS = 0 35 for copper, h 1s the thickness, and D the diameter of the pipe For a fundamental frequency of 17 kHz and a disc diameter of 15 mm, a disc thickness of 0 5 mm IS required To achieve this, a circular flat of dlameter 15 mm was formed on a sectlon of a 22 mm diameter copper pipe which has been thinned to 0 5 mm Details of this procedure are gven m the Appendix Two transducer devices were used to dnve the flat with plezoelectrlc (PZT) and electromagnetic (EMT) operation The mechanism of electromechanical transduction m a PZT crystal used in a transducer IS on a molecular scale and, m terms of its sensltlvlty and efficiency at higher frequenaes, it IS usually preferred to other methods The mechanical amplitude that can be generated by a PZT element 1s hrmted, so that it 1s unsuitable for low-frequency applications where the displacement excursions are appreciable However, the amplitude can be amphfied and the frequency of osclllatlon reduced by bondmg the PZT element to a metal diaphragm of calculable fundamental frequency of vlbratlon, as dlscussed above In this case, the PZT element and the passwe matenal to which it is bonded constitute a compound resonant system whose osclllatlons give nse to alternatmg pressure waves m the fled that can, m turn, nutlate waves on both &rectlons An EMT actuator m the form of an E-shaped core wth a co11 on its centre leg carrying both a c and d c currents can be mounted very close to, but not touchmg, the flat on the pipe An alternating current m the wmdmg generates an alternatmg magnetomotlve force m the region of the flattened pipe m the skm depth of the metal The magnetic field 1s prevented from further penetration by an Image current of the current m the
The expernnental PZT transducer discussed m this work was made by bondmg a thm PZT ceranuc piece of 5 mm diameter to the flat on the pope to form a metal disc flexural resonator It was then driven by an r f power amplifier, while the point of resonance was detected by a slmllar flat at a certain separation on the pipe from the transmitting flat The experimental EMT transducer was made from one half of a gapped RM 6R (4146) inductor pot core of ferroxcube matenal (grade A13), wound wth an enamelled copper wire of 0 25 mm duuneter (swg 33) The core was chosen for Its s=e (active cross-sectional area comparable with that of the flat on the plpc) and for its ablhty to operate at a frequency of up to 700 kHz The mounting was such that the separation between the actuator and the flat on the pipe was less than 1 mm The actuator was driven by a clrcmt comprmng a band-pass filter, an impedance transformmg network, an r f power amplifier, a signal generator, and a d c supply The detecting circuit consisted of the detectmg actuator, an impedance-matching network, an a c differential amplifier, a band-pass filter, and an osalloscope The followmg mvestlgatlons of performance usmg different transducer combmatlons were conducted (a) PZT-driven flat recelvmg from another PZTdnven flat, (b) PZT-driven flat receiving from EMT-driven flat, (c) EMT-dnven flat recelvmg from PZT-dnven flat The results obtamed from these mvestlgatlons are shown m Figs 1 and 2 and they are discussed below
Experimental results
Figure 1 shows the responses of signals transnutted from a PZT flat to another PZT Rat and also to an
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-120 0
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Fig I Comparmg the responses of a PZT-dnven flat to another PZT-driven flat (1) v&h that of an EMTdnven flat to a PZTdnven flat (2) (pressure axs scahng factor mcreased 20 times)
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Fig 2 Comparmg the responses of a PZT-driven flat to an EMT-drwen flat (1) w&h that of an EMT-driven flat to a PZTdriven flat (2) (pressure axis scahng factor Increased 20 times)
flat (the pressure amphtude axis scalmg ratio being mcreased 20 times) wth still water m the pipe at approxnnately room temperature The response to a PZT flat shows two resonant peaks centred about 17 and 19 kHz The 17 kHz resonance 1s the calculated fundamental resonance of the flat, while the 19 kHz resonance may have been a result of reflections from distant bends m the piping network The response to an EMT flat shows the same mode shape but IS shfted towards lower frequency values In particular, the mam resonance 1s seen to occur at a frequency value of about 15 5 kHz This 1s not surpnsmg, as the effect of bonding a PZT element to the flat 1s to Increase Its resonance frequency through the increase of its stiffness At the operatmg frequency of 17 kHz, the mechamcal resonance frequency of the disc can be considered to be stiffness controlled The plots of Fig 2 show the responses of a PZT flat to an EMT flat and of an EMT flat to a PZT flat (the pressure axis scaling ratio increased 20 times) This and
EMT
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Fig 3 Comparmg the sensltwty and hnearlty of a PZTdnven flat (top trace) v&h that of an EMT-driven flat (bottom trace) on a 22 mm diameter copper pipe filled wth water at room temperature
the results of Fig 1 indicate that the PZT flat shows identical responses to excltatlons from either another PZT flat or an EMT flat The sensltlvlty plot, as shown m Fig 3, estabhshes the PZT device as being more sensitive than the EMT device by about 70 dB It also shows that the PZT device 1s more linear (slope = -0 06) than the EMT device (slope = -0 12) In the expenments discussed above, it was not possible to detect, Hnth an EMT device, pressure waves from another EMT device because, as can be seen on Fig 3, the sensltlvlty was down to over -200 dB Detection could have been possible if the overall sensitivity were raised to about - 100 dB The ferroxcube core used could only support 40 mT (400 G) of polarlzlng field, whereas to increase the sensltlvlty to - 100 dB would require a field of over 400 mT (4000 G) Soft magnetic matenals of rheometal, allenol, or supermalloy can be used to provide higher field mtensltles Alternatively, permanent magnets of Almco material can be used to provide d c fields m the range 400 mT- 1 2 T (5000- 12 000 G) The borderhne between the two transducers m the size range of the copper pipe considered 1s probably about 25 mm diameter, above which the EMT actuator 1s expected to be more efficient and below which the PZT actuator should show gams m efficiency
Flow measurements The conventional system for measurmg fluid tlow relies on a par of transducer assemblies posltloned some distance away from each other along the pipe Using established measurmg techmques, the net flow can be derived from the tnne, phase tierence, or frequency &fference of pulses transnutted m the dlrectlon for and agamst the flow
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Fig 4 Schematic of electrical configuration of the phase-lockedloop momtormg arrangement pd = phase detector, amp = amphfiex, lpf = low pass filter, osc = oscillator
Freq/kHz
Rg 6 Pressure amplitude as a function of frequency, showmg resonant modes of the system wth air m the pipe at room temperature
Fig 5 Schematic of a self-oscdlatmg system for flow measurements usmg long acoustic waves Freq/kHz
Here, a pair of long-wave transducers has been used,
developed as discussed above, with a flow-measunng cell, as shown schematically m Figs 4 and 5, whose standing-wave characterlstlcs are known and can be controlled The harmonic equations for both the even and the odd harmonics for such cells are aven respectively as f, = ncih 2n+lc S, =~z,
n =
1,2, 3,
(2)
n =0, 1,2,3,
(3)
wheref, IS the frequency, c 1s the velocity of sound m the fluid, and n an integer The charactenstlcs for still air and water at room temperature in a 22 mm copper pipe flow cell of length 1070 mm were investigated experunentally, and they are shown m Figs 6 and 7 where, for example, the mam resonance peaks of 8 86 kHz for au and 6 21 kHz for water can be seen as obeying the odd-harmonic equation (eqn (3)) of the tube when n = 28 for air and n = 4 for water The main mode for air 1s not suitable m this apphcatlon because the wave does not appear to be guided by
Fig 7 Pressure amphtude as a function of frequency, showmg resonant modes of the system urlth water m the pope at room temperature
the pipe (the wavelength m air 1s comparable with the duuneter of the pipe) A smtable mode can be found m eqn (2) when n = 21, to gve a resonance of 6 63 kHz (6 64 kHz was obtamed experunentally) This produces a wavelength m an of approxunately two and a half tnnes the diameter of the pipe The flow cell used m this expenment ~11 accommodate approximately ten and a half wavelengths at this mode, and ~11 permit an effective averagmg of the flow rate over its entire length The sensitivity of a smtable resonance frequency to flow can be measured m a number of ways, two of which are the phase/frequency-locked loop technique shown m Fig 4, and the self-osctiatmg technique shown m Fig 5 [7] In the phase-locked-loop technique, an oscillator frequency, f(o), which dnves a transnutter of acoustic waves is automatically adjusted to match the frequency of an input signal, f(i), from a receiver of acoustic waves m the flow cell This circuit forces the oscillator
Theory
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Flowrate/tltres
c o) 1 <.>
1
1 I
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Rg 8 Calculated and expermental frequency changes as a functlon of volume flow rate mth water as the Rmd
to a frequency whose period of oscdlatlon IS a function of the tune-of-fhght of the acoustic wave from one end of the flow cell to the other, lrrespectlve of the state of flow m the cell The differential frequency of the upstream and downstream transmaslon IS equvalent to the differential frequency of the conventional ‘smgaround’ frequency technique and IS a function of the flow rate The dflerentlal frequency at different volume flow rates through the flow cell was measured with a vanable-area flow indicator as a reference The calibration results and the theoretical predlctlons are shown m Fig 8, where it can be observed that although there IS no change of linear sensitivity, there 1s a change of zero bias by about 1 5 Hz This offset 1s not flow dependent and can be ignored The constant bias IS due to the improper matching of the transducers dunng production A very careful matchmg technique could therefore be adopted m a more developed system to reduce thrs bias to an msign&ant value A test of performance repeatability at 1 5 l/mm gves a repeatablhty value of +O 19 Hz for the 95% confidence limit (meaning only 5% of a set of frequencydifference readings made at any rate of volume flow under the same condlhons wdl have a ddference between them of more than 0 19 Hz) Hence, m terms of the accuracy, only 5% of the readings w111he outside the range 1 30-l 70 l/mm This can be unproved by using a standard test ng and by observmg close tolerances durmg the production of the transducers As shown m Fig 5, a combmatlon of the transnutter, the receiver, the acoustic path, and a linear amphfier constitutes the basis of the self-osclllatmg technique, m which the oscillation frequency 1s defined precisely by the phase relationstip between the transnutted and the received signals Since this phase relation unll vary with the flow velocity, the frequency of osallatlon gves a
measure of the flow The development of this techmque 1scontmumg, mth prehmmary results at this stage of its development being beyond the scope of this paper A workable unit ill be essentially sunple wth low device counts, in particular, m its construction The ments for nnplementmg flow measurements usmg a measurement cell of the type described above are numerous, for example (1) The resonatmg system reduces attenuation between the transrmtter and the receiver, a condition that 1s of unmense importance when measuring gas flow (u) The flow meter does not require a specified amount of pipe run to deliver its stated accuracy (111)It acts as a narrow-band filter to any extraneous signal that may anse from control taps or sometunes from the acoustic effects of plumbers working on an adJacent site
Energy conservation Heat and hot-water provlslon to dwellings, mdustnal, and commercial premises are now often metered and charged m a slrmlar way to the electnc and the gas services The chargmg of flat rates for heat and hotwater semces does very httle to encourage consumers to conserve energy The result 1s that there IS a conslderable waste of energy, which often leads to an increase m generating costs and charges, or to the lowenng of standards m order to reduce the financlal comnutments of the provldmg authonty It would be beneficial, therefore, to those who receive their heating and hot water from dlstnct authontles that a cheap but effective means for chargmg for these services according to the amount expended m mdlvldual prenuses should exist The measurement of heat involves the measurements of two vanables temperature and water flow The system described m this paper can provide adequate mdlcatlon of heat consumption takmg mto account these variables The measurement of the water throughput volume can be carned out on the flow or return water flow meters m a manner described m the previous Se&on, while the determination of the temperature difference can be done through the assessment of the resonance frequency difference between the flow and the return water flow meters such that the rate of heat expended can obey the followmg mathematical relatlonshlp
where dQ/dr = the rate of heat expended or supplied, p = density of water, L = length of flow cell, c,, = speed of sound m water at absolute zero, ffl = the resonance
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frequency of the flow-path flow meter, f,, = the resonance frequency of the return-path flow meter, and Af = the frequency change between an upstream or a downstream transmlsslon m either the flow- or the return-path flow meter, and A 1s a constant A specified heat-flow ng IS necessary to conduct specific expernnents, but the likely performance can be mferred from the flow measurement results
Discussion It has been shown that an appropnately dlmensloned flat formed on a section of a pipe carrying a fluid, and driven by either a plezoelectrlc (PZT) or an electromagnetlc (EMT) actuator can reduce the non-propagatmg loop resonance of a cyhndncal pipe and excite a wave that 1s guided m the fluid wlthm the pipe The PZT-driven long-wave transducer was found to be more sensltlve and more lmear than the EMT-dnven transducer, which showed better noise-reJection charactenstlcs The guided wave can be used to measure the volume flow of high-value fluids m small-diameter pipes m the size range 5- 100 mm In fact, It has permitted prehmlnary mvestigatlons of flow measurements usmg water as a test fluid m a 22 mm diameter copper flow cell m which known and controllable standing-wave patterns have been generated The results have shown good agreement with simple theoretical predlctlons The posslblhty of using a combmatlon of two longwave transducers and a standing-wave flow cell m the metermg of heat and hot-water services m mdlvldual premises has also been discussed
7 E S Ikpe, G G Scarrott, J P Weight and K T V Grattan, A standmg wave flow measurement system for small diameter pqxhnes usmg long acoustic waves, Rev Scr Instrum , m press
Appendix 1 Transducer fabrrcatlon &tads
The transducer sectlon was made from a 22 mm diameter copper pipe of length 200 mm before being connected to the rest of the system by two 22 mm straight couplers The copper pipe has a wall thickness of approximately 1 mm A section of this pipe was thinned m a lathe to the required thickness of 0 5 mm The thinned section was 45 mm long and started at 77 mm from either end of the pipe (Fig Al) Followmg expenmentation with various methods, a Jig was made to stamp a flat of the requned shape and dlmenslons on the thinned pipe sectlon (Figs A2-A4) The Jig comprised a rectangular block of alummmm of dlmenslons 100 mm x 85 mm x 50 mm (Fig A2),
-T
Pomm
-1 -G-
-nh
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Rg Al Cross se&on of a 22 mm copper pipe showmg a thmned resonatmg section
Acknowledgement The authors are pleased to acknowledge the support of the Science and Engmeermg Research Council (SERC) m this work
References 1 J Hemp, Theory of transit time ultrasomc flowmeters,J Sound V&r, 84 (1982) 44-48 2 B Robertson, Flow and temperature profile mdependence of flow measurements usmg long acoustic waves, ASME Trans , 106(1984) 18-20 3 H Lechner, Ultrasonic measurement of volume flow mdependent of velocity hstnbutlon, Acta IMEKO, (1982) 279-288 4 E S Ikpe, G G Scarrott, J P Weight and K T V Grattan, Generation and detectIon of long waves m a flmd m a pqx, Report to Sctence and Engrneerrng Research Councrl, UK, 1993 5 J E Potnck and B Robertson, Long wavelength acoustic flowmeter, US Patent No 4 445 389 (1984) 6 J Randeraat and R E Settermgton (eds ), Ptezoelectnc Ceramcs, Mullard, London, 1974, pp 81-86
ct 22
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Fig A2 A spht block of alurnmmm wth a 22 nun hole through Its length and a 45 mm x 18 mm rectangular hole through Its thickness
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lllalun Fig A4 A side view of a spht rod of steel with a thmned section of length 45 mm and a rectangular flat of length 35 mm
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Fig A3 An ahnnmnun block with a circular button of 15 mm diameter attached to Its tapered end
a flatter block of alummnnn of dnnenslons 62 mm x 44 mm x 17 mm at the end of which was attached a metal button of darneter 15 mm and thickness 7 mm (Fig A3), and a steel rod of length 110 mm and dlameter 21 mm (Fig A4) The block of Fig A2 has a circular hole of 22 mm diameter right through its length, and a rectangular hole of dnnenslons 45 mm x 18 mm through its thlckness This block 1s split into two equal halves along Its thickness and the halves held together by four screws It can be noted that the circular hole IS made equal to the 22 mm pipe diameter, while the length of the rectangular hole IS made equal to the length of the thmned sectlon of the pipe Also the flatter block of Fig A3 fits mto the rectangular hole of the thick block
On the steel rod of Fig A4 was formed a rectangular flat of dnnenslons equal to the rectangular hole on the thick block The rod was then split mto two halves such that there 1s half of the rectangular flat on each section of the rod In order to form the reqmred flat on the pipe, the rod of Ag A4 was inserted mto the pipe of Fig Al The unit was then inserted into one half of the block m Fig A2, wth the thinned section of the pipe aligned to the flat on the rod and the rectangular hole m the block The second half of the block was then secured to the arrrangement by four screws, while the rod m the pipe was held m place by a heavy stud The block of Fig A3 was attached m a press and then lowered through the rectangular hole m the block to press the circular flat on the thmned section of the pipe TUB exercise obviously distorts the cross section of the pipe and it would have been nnposslble to remove the steel rod from the pipe had it not been spht m two The steel rod ensured that the pipe &d not gve m to the pressure of the press, while the block ensured that the pipe remams fairly straight after the flat-formmg operation