sensors Article
A Novel Ultrasonic Method for Liquid Level Measurement Based on the Balance of Echo Energy Bin Zhang 1,2 , Yue-Juan Wei 3 , Wen-Yi Liu 1,2, *, Yan-Jun Zhang 1,2, *, Zong Yao 1,2 , Liang Zhang 1,2 and Ji-Jun Xiong 1,2 1
2 3
*
Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China; [email protected] (B.Z.); [email protected] (Z.Y.); [email protected] (L.Z.); [email protected] (J.-J.X.) Science and Technology on Electronic Test & Measurement Laboratory, North University of China, Taiyuan 030051, China Software School of North University of China, Taiyuan 030051, China; [email protected] Correspondence: [email protected] (W.-Y.L.); [email protected] (Y.-J.Z.); Tel.: +86-351-3557-385 (W.-Y.L. & Y.-J.Z.)
Academic Editor: Xiaoning Jiang Received: 13 February 2017; Accepted: 24 March 2017; Published: 28 March 2017
Abstract: This study presents a novel method for determining the liquid level from the outside of a sealed container, which is based on the balance of echo energy received by two receiving sensors. The proposed method uses one transmitting transducer and two receiving sensors that are encapsulated in a coupling plane and arranged by certain rules. The calculation and comparison of echo energy are grounded on the difference ultrasonic impedance between gas and liquid media. First, by analyzing the propagation and attenuation characteristics of ultrasonic waves in a solid, an acoustic model for calculating the echo energy is established and simulated in MATLAB. Second, the proposed method is evaluated through a series of experiments. The difference and ratio of echo energy received by two receiving sensors are calculated and compared under two different coupling conditions. Two kinds of the sensors that are arranged by different rules are selected for measuring the liquid level, and the measurement are analyzed and discussed in detail. Finally, the experimental results indicate that the proposed method can meet the proposed accuracy requirements and can effectively solve the problems caused by some poor coupling conditions. Keywords: ultrasonic impedance; balance; echo energy; coupling; matching layer
1. Introduction In fields such as petroleum, chemical, and aerospace, the real-time monitoring and accurate measurement of the liquid level in a sealed container are important for the industrial automation and safety production [1,2]. In actual industrial production, an appropriate measurement method should be selected to suit the specific environment and safety requirements [3,4]. There are several traditional liquid level measurement methods [1–6], of which the technologies are stable and reliable and the measurement results are accurate. However, these methods usually require some sensors or all of detection equipment to be installed inside a container in advance. Some special industries require a container to be stored with high temperature, high pressure, inflammable, explosive, highly corrosive, or strong, volatile liquid inside. It is easy for a leakage accident to occur, and after a containment failure, maintenance is difficult and costly. For these reasons, some scholars and institutions in the United States began in the 1980s to study and use new technologies based on fiber optics, ultrasound, lasers, and gamma rays for liquid level measurement. Among these, ultrasonic detection technology can achieve a true sense of non-contact Sensors 2017, 17, 706; doi:10.3390/s17040706
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container. Therefore, ultrasonic technology for liquid level detection has been developed rapidly in and non-immersion measurement without damaging the physical structure and integrity of a container. recent years. Therefore, ultrasonic technology for liquid level detection hason been developed rapidly can in recent years. Generally, the liquid level measurement methods based ultrasonic technology be divided Generally, the liquid level methodsas based on ultrasonic technology be divided into four types according to themeasurement realization principle, described in literature [1]. Allcan of them have into four of types according to theand realization described in literature [1]. All of them strengths ultrasonic detection applyingprinciple, conditions.asThey also have some weaknesses, such as have strengths of ultrasonic detection and applying conditions. They also have some weaknesses, high coupling requirements between sensors and the surface of the container wall. In actual such as high coupling requirements between surface of the container wall. In of actual measurement, an appropriate coupling agentsensors shouldand be the chosen according to the material the measurement, an appropriate agentlayer should be chosen according to thetomaterial of the container, and the thickness ofcoupling the coupling should be adjusted according experimental container, the coupling layer are should be adjusted according to measuring experimental results results so and thatthe thethickness incidentofultrasound waves consistent throughout the process, so that the waves areliquid consistent throughout thethe measuring process, because the because theincident premiseultrasound is to determine the level by comparing impedance characteristics of premise positions. is to determine the liquid level by comparing the impedance characteristics of different different Otherwise, the measuring result is inaccurate or meaningless. positions. the measuring result is inaccurate or meaningless. WhenOtherwise, a beam of ultrasound is transmitted from above and below the liquid level respectively, When a beam echo of ultrasound transmitted fromdifferent above and below the liquid level respectively, the two reflected energies isare significantly because of the different ultrasonic the two reflected echo energies are significantly different because of the different ultrasonic impedance impedance between gas and liquid media in a container. This study presents a novel measurement betweenThe gasproposed and liquid mediauses in athe container. This study presents a novel measurement method. method. method balance of echo energy received by two sensors to determine Theliquid proposed method usesoutside the balance echo energy received two sensors to determine the level from the of a of sealed container. It canbysolve the problems causedthebyliquid bad level frombetween the outside of a sealed container. It can solve problems by bad and coupling between coupling sensors and the container wall, andthe can enhancecaused the stability reliability of sensors and the container wall, and can enhance the stability and reliability of measurement. measurement. In the the proposed proposed method, method, three three round round plate plate ultrasonic ultrasonic sensors sensors are are used used and and arranged arranged as as shown shown In Figure 1, 1, and and meet meet the the following following conditions: Figure
Figure d = r +r . Figure1.1.The Thearrangement arrangementrules rulesof ofthree threesensors: sensors: (a) (a) dd1 = = 0; 0; and and (b) (b) d 1 = r1 + r2 .
• • • •
The transducer S is used as an ultrasonic transmitter. The other two sensors, S and S , are The transducer S is used as an ultrasonic transmitter. The other two sensors, S1 and S2 , are used used as receivers; 0 as receivers; The distances d and d meet the conditions 0 ≤ d ≤ r + r , 2r ≤ d ≤ (4r + 2r ). The two The distances d and d meet the conditions 0 ≤ d1 ≤ r1 + r2 , 2r2 ≤ d2 ≤ (4r1 + 2r2 ). The two receiving sensors1 S and2 S are arranged symmetrically along the horizontal coordinate axis; receiving sensors S1 and S2 are arranged symmetrically along the horizontal coordinate axis; Three sensors are placed on the same coupling plane and encapsulated in a rectangular plastic Three sensors box with epoxy;are placed on the same coupling plane and encapsulated in a rectangular plastic box with epoxy;process, the sensors are moved along the longitudinal direction on the surface of In the detection the detection aIn container wall. process, the sensors are moved along the longitudinal direction on the surface of a container wall.
Measuring principle: As shown in Figure 2, when using the transducer S to emit a beam of Measuring principle: As shown in Figure 2, when using the transducer S0 to emit a beam of ultrasonic waves perpendicularly to the outer surface of a container wall, both of the receiving ultrasonic waves perpendicularly to the outer surface of a container wall, both of the receiving sensors sensors S and S could detect echoes reflected by the inner surface if the wall thickness L is less S1 and S2 could detect echoes reflected by the inner surface if the wall thickness L is less than the than the length of the sound field. Because they are geometrically symmetrical to the transmitting length of the sound field. Because they are geometrically symmetrical to the transmitting transducer transducer S , if the reflection boundary conditions at the inner surface are consistent, the echo S0 , if the reflection boundary conditions at the inner surface are consistent, the echo energy received by energy received by the two receiving sensors should be equal in magnitude. The different ultrasonic the two receiving sensors should be equal in magnitude. The different ultrasonic impedance between impedance between the gas and liquid media will make the reflection and transmission of sound the gas and liquid media will make the reflection and transmission of sound waves different at the waves different at the inner surface. Therefore, the acoustic boundary conditions will be changed
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Sensors 2017, 17, 706 3 of 12 inner surface. Therefore, the acoustic boundary conditions will be changed continuously when the continuously when theStransmitting transducer S is moved near the liquid level, and the balance of transmitting transducer is moved near the liquid level, and the balance of echo energy received by 0 continuously when the transmitting transducer S is moved near the liquid level, and the balance of echo energy received by the two receiving sensors S and S will be destroyed. In this research, the the two receiving sensors S1 and S2 will be destroyed. In this research, the balance is used to determine echo energy received by the two receiving sensors S and S will be destroyed. In this research, the balance is used to determine the liquid level. thebalance liquid level. is used to determine the liquid level.
Figure 2.2.The proposed method. method. Figure Themeasuring measuringprinciple principle of of the proposed Figure 2. The measuring principle of the proposed method.
Advantages: In the proposed method, the two receiving sensors are arranged along the same Advantages: receivingsensors sensorsare arearranged arrangedalong along same Advantages:InInthe theproposed proposed method, method, the the two two receiving thethe same coupling plane, and the balance of echo energy received by the two receiving sensors is the only thing coupling plane, and the by the thetwo tworeceiving receivingsensors sensorsisis the only thing coupling plane, and thebalance balanceofofecho echoenergy energy received by the only thing that needs attention. In other words, the ratio of two received echo energy at the same position is that needs attention. In other words, the ratio of two received echo energy at the same position is that needs attention. In other words, the ratio of two received echo energy at the same positionwhat is what we care about, rather than the magnitude of echo energy value. The proposed method reduces wewhat care we about, magnitude of echo energy value. TheThe proposed method reduces care rather about, than ratherthe than the magnitude of echo energy value. proposed method reducesthe the coupling requirements of transmitting sensor, and enhances the reliability, stability, and the coupling requirements of transmitting and enhances the reliability, and coupling requirements of transmitting sensor,sensor, and enhances the reliability, stability,stability, and sensitivity sensitivity of detection. sensitivity of detection. of detection. 2. Theory and Methods 2. Theory and Methods 2. Theory and Methods 2.1. The Energy Circle 2.1.2.1. The Energy Circle The Energy Circle According to the model and measurement of Schmerr [7,8], the sound field of a round piston Accordingtotothe themodel modeland andmeasurement measurement of Schmerr piston According Schmerr[7,8], [7,8],the thesound soundfield fieldofofa around round piston sensor in a solid medium has two different parts [9,10]. In the near field, the beam can maintain a sensor in a solid mediumhas hastwo twodifferent different parts parts [9,10]. In the near field, the beam can maintain a sensor in a solid medium In the near field, the beam can maintain cylindrical shape to transmit because of its smaller divergence angle. In the far field region, the beam a cylindrical shape to transmit because of its smaller divergence angle. In the far field region, the beam cylindrical shape because ofangle, its smaller divergence In the far field region, the beam propagates withtoatransmit certain divergence as shown in Figureangle. 3. propagates with a certaindivergence divergenceangle, angle,as asshown shown in in Figure Figure 3. propagates with a certain 3.
Figure 3. The sound field of a 1 MHz, 20 mm diameter round piston transducer in an aluminum alloy Figure The soundfield fieldofofaa11MHz, MHz, 20 20 mm mm diameter diameter round anan aluminum alloy Figure 3. 3. The sound roundpiston pistontransducer transducerinin aluminum alloy as calculated with a Multi-Gaussian Beam Model. as calculated with a Multi-Gaussian Beam Model. as calculated with a Multi-Gaussian Beam Model.
The sound field was calculated by using Multi-Gaussian Beam Model [11–13], which can The sound field was calculated by using Multi-Gaussian Beam Model [11–13], which can simulate the sound field of a transducer in 2D and 3D. The ultrasonic wave frequency was 1 MHz, The sound fieldfield wasof calculated by in using Multi-Gaussian Beam Model [11–13], simulate the sound a transducer 2D and 3D. The ultrasonic wave frequency waswhich 1 MHz,can the diameter of the transducer was 20 mm, the wall material was aluminum, in which the simulate the sound field of a transducer in 2D and 3D. The ultrasonic wave frequency was the diameter of the transducer was 20 mm, the wall material was aluminum, in which1 MHz, the compressional wave speed was 6300 m/s, the shear wave speed was 3100 m/s, and the ultrasonic compressional wave speed was 6300 m/s, the shear wave speed was 3100 m/s, and the ultrasonic
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the diameter the transducer was 20 mm, the wall material was aluminum, in which the compressional Sensors 2017, 17,of 706 4 of 12 wave speed was 6300 m/s, the shear wave speed was 3100 m/s, and the ultrasonic impedance 5 gm/cm2 ·5s. The 2length of the near field N and the diffusion angle β are given by was 17 × 10was impedance 17 × 10 gm/cm ·s. The length of the near field N and the diffusion angle β are given Equations (1) and (2),(2), respectively [14].[14]. by Equations (1) and respectively r2 N= r (1) (1) N = λc λ 1.22λc (2) β = arcsin 1.22λ (2) β = arcsin 2r 2r where λc is the wavelength of ultrasonic waves in a metal wall, r is the radius of the sensor. the wavelength ultrasonic in a metalbeam wall, will r is the radius of theregion sensor.on inner where λ isFigure From 3, it can beofinferred thatwaves the ultrasonic form a circular From Figure 3, it can be inferred that the ultrasonic beam will form a circular region on inner surface of a container wall after a propagating distance, and the beam energy is mainly concentrated surface of a container wall after a propagating distance, and the beam energy is mainly concentrated in this region. The projected circular region is referred to as the energy circle, of which the diameter is in this region. circular region is referred expressed by dThe andprojected can be calculated by Equation (3): to as the energy circle, of which the diameter is expressed by d and can be calculated by Equation (3): ( dd= L≤ = 2r 2r((L ≤N N)) (3) (3) d d==22[r − N tan L > N) N) [r ++(L ) (L − N) tanββ]] ((L 2.2. Sound Pressure Distribution at Any Point outside the Axis 2.2. Sound Pressure Distribution at Any Point outside the Axis As shown in Figure 4, P(x, y, z) is a point outside the axis of the round piston sensor, the distance As shown in Figure 4, P(x, y, z) is a point outside the axis of the round piston sensor, the distance from the center O(0, 0, 0) of the sensor to the point P(x, y, z) is marked by R = D(O, P). The angle from the center O(0,0,0) of the sensor to the point P(x, y, z) is marked by R = D(O, P). The angle between R and the x-axis is denoted by θ. Then, according to the Kirchhoff integral theorem [15–17], between R and the x-axis is denoted by θ. Then, according to the Kirchhoff integral theorem [15– the sound pressure at the point P can be calculated as 17], the sound pressure at the point P can be calculated as 2 πa 2J1(kasinθ) (kasinθ) πa 2J p(p(R, R, θθ) = (4) ) = ∙ ·pp0 (4) λR kasinθ λR kasinθ
theinitial initialsound soundpressure pressure sound source, is the wavelength of ultrasonic waves where pp0 isisthe where ofof thethe sound source, λ isλthe wavelength of ultrasonic waves in a in a medium, a radius is the radius of the and sensor, k is the waveJ1number; J kind is theoffirst first medium, a is the of the sensor, k is and the wave number; is the first first kind orderof Bessel order Bessel The geometric meaning of other variables is shown function. Thefunction. geometric meaning of other variables is shown in Figure 4. in Figure 4.
4. Calculating Calculatingthe theacoustic acoustic field characteristics a round transducer at anyoutside point Figure 4. field characteristics of a of round pistonpiston transducer at any point outside axis according to the Kirchhoff integral theorem. the axis the according to the Kirchhoff integral theorem.
Because of the interference interference in the near near field field of of aa round round piston piston transducer, transducer, Equation Equation (4) (4) is is valid valid Because of the in the only in in the the far far field, field, which which requires requires the the wall wall thickness thickness to meet the condition LL > only to meet the condition > NN in in aa detection. detection. This requirement can be achieved by adjusting the near field length N for a given container. This requirement can be achieved by adjusting the near field length N for a given container. Equation (1) Equation (1) demonstrates that the radius of the transducer and the ultrasound wave length in a demonstrates that the radius of the transducer and the ultrasound wave length in a container wall are container wall are critical factors, and the latter is associated with the transmitting frequency and the critical factors, and the latter is associated with the transmitting frequency and the wall material. wall material. 2.3. Analysis of Echo Energy According to the basic knowledge of acoustics, ultrasonic waves will be refracted and reflected at an interface with discontinuous impedance, which follows the refraction and reflection principle of sound waves.
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2.3. Analysis of Echo Energy According to the basic knowledge of acoustics, ultrasonic waves will be refracted and reflected at an interface with Sensors 2017, 17, 706 discontinuous impedance, which follows the refraction and reflection principle 5 ofof 12 sound waves. As shown in Figure 5, when the transmitting transducer S0 is excited to transmit an ultrasonic beam into the wall, part of the ultrasonic beam will be reflected by the interface 2, and the echoes will be oscillated repeatedly between interfaces 1 and 2 until they decay to zero. Another part of the beam will transmit into the gas-liquid medium in container, of which the energy may decay to zero in propagating process, or may penetrate the gas-liquid medium and be reflected by interfaces 3 and 4. All of these reflected echoes can be detected by the two receiving sensors S1 and S2 that are attached to Sensors 2017, 17, 706 5 of 12 the outer surface of the container wall.
Figure 5. The process of an ultrasonic beam propagating in a container. S is a transmitter, S and S are two receivers, 1,2,3,4 represent the four interfaces of the container.
As shown in Figure 5, when the transmitting transducer S is excited to transmit an ultrasonic beam into the wall, part of the ultrasonic beam will be reflected by the interface 2, and the echoes will be oscillated repeatedly between interfaces 1 and 2 until they decay to zero. Another part of the beam will transmit into the gas-liquid medium in container, of which the energy may decay to zero in propagating process, or of may penetratebeam the gas-liquid medium and beSreflected by interfaces Figure 5. The process an ultrasonic propagating in a container. is a transmitter, S and 3S2and 4. Figure 5. The process of an ultrasonic beam propagating in a container. 0S is a transmitter,1 S and All of these reflected echoes can be detected by the two receiving sensors S and S that are attached are two receivers, 1,2,3,4 represent the four interfaces of the container. S are two receivers, 1,2,3,4 represent the four interfaces of the container. to the outer surface of the container wall. Asshown shown inFigure Figure6,6,in inthe thedetection detectionprocess, process,when whenthe thetop topof ofthe theenergy energycircle circleexceeds exceedsthe the As in Figure 5, when the transmitting transducer S is excited to transmit an ultrasonic liquid level, the exceeding height is represented by ∆d and 0 ≤ ∆d ≤ d. Assuming that the total area liquid level, the exceeding is represented by ∆d and 0 ≤ by ∆d the ≤ d. Assuming thatthe theechoes total area beam into the wall, part of height the ultrasonic beam will be reflected interface 2, and will of the energy circle is A, the area of the energy circle above the liquid level is denoted by A andlet let of energyrepeatedly circle is A, between the area interfaces of the energy circle above liquid denoted by of ATthe , ,and bethe oscillated 1 and 2 until theythe decay to level zero. is Another part beam ⁄ r = A A . rwill transmit into the gas-liquid medium in container, of which the energy may decay to zero in s =A T /A. propagating process, or may penetrate the gas-liquid medium and be reflected by interfaces 3 and 4. All of these reflected echoes can be detected by the two receiving sensors S and S that are attached to the outer surface of the container wall. As shown in Figure 6, in the detection process, when the top of the energy circle exceeds the liquid level, the exceeding height is represented by ∆d and 0 ≤ ∆d ≤ d. Assuming that the total area of the energy circle is A, the area of the energy circle above the liquid level is denoted by A , and let r = A ⁄A.
Figure Figure 6. 6. Calculating Calculating the the echo echo energy energy received received by by the the two two receiving receiving sensors sensors SS1 and andS2S. .
In Figure 6, when taking ρ = d/2 and 0 ≤ φ ≤ π, we can get the value of ∆d and the ratio r by Equations (5) and (6). d ∆d = (1 − cos φ) 2 1 r = (φ − sin φ cos φ) Figure 6. Calculating the echo energyπreceived by the two receiving sensors S and S .
(5) (6)
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In Figure 6, when taking ρ = d/2 and 0 ≤ ϕ ≤ π, we can get the value of ∆d and the ratio rs by Equations (5) and (6). d (1 − cos ϕ) 2
(5)
1 (ϕ − sin ϕ cos ϕ) π
(6)
∆d = rs =
When 0 ≤ ∆d ≤ d, the energy circle is divided into two parts by the liquid level, which makes the acoustic boundary conditions of the two parts different. When an ultrasonic beam propagates first to interface 2, the sound pressure in two parts of energy circle are represented by Pg and Pl receptively, and assuming Pg > Pl , as shown in Figure 6. Here, the energy circle can be approximately regarded as a round transmitting transducer. Assuming that there is a point P(ρ, ϕ) in the upper part of the energy circle, and with the energy circle moving up, the average sound pressure at the point P increases from Pl to Pg . According to Equation (4), the sound pressure of the two receiving sensors S1 and S2 can be obtained by integrating all the points in the red part of the energy circle, which can be described approximately by Equations (7) and (8) ∆ps1 (h1, θ) =
π(d/2)2 ·rs λh1
!
∆ps2 (h2, θ) =
π(d/2)2 ·rs λh2
!
2J1 (k(d/2) sin θ) · pg − pl ·πr22 k(d/2) sin θ
(7)
2J1 (k(d/2) sin θ) · pg − pl ·πr22 k(d/2) sin θ
(8)
where ρ is the polar radius, ϕ is the polar angle, θ is the angle between R1 (or R2) and the x-axis, h1 = D(P, S1 ), h2 = D(P, S2 ), R1 = D(O, S1 ) = h21 + ρ2 − 2 sin θ cos ϕ, R2 = D(O, S2 ) = h22 + ρ2 − 2 sin θ cos ϕ, Pg = P0 e−αL Rmg and Pl = P0 e−αL Rml , Rmg represents the reflection coefficient at the upper part of the energy circle, Rml represents the reflection coefficient at the lower part of the energy circle. Furthermore, it is assumed that the echo energy in the wall will decay to a very small amount after n times, which can be negligible relative to the total energy received by receiving sensor. Therefore, when the sound beam is reflected to the outer surface of the wall at the n times, the total pressure of S1 and S2 can be derived as following equations: ∑ ps1 (h1, θ) = ∑ ps2 (h2, θ) =
π( d2 ) λh1
π(d/2)2 λh2
2
h
h
2J1 (k(d/2) sin θ) k(d/2) sin θ
2J1 (k(d/2) sin θ) k(d/2) sin θ
i
i
n n −1 −2iαL −1 −2iαL e + (1 − rs )· ∑ Riml Rima e ·P0 ·πr22 · rs · ∑ Rimg Rima i=1
n n −1 −2iαL −1 −2iαL e e + (1 − rs )· ∑ Riml Rima ·P0 ·πr22 · rs · ∑ Rimg Rima i=1
(9)
i=1
(10)
i=1
where Rma represents the reflection coefficient at interface 1, α is the attenuation coefficient of a container, and L is the thickness of a container wall. In conclusion, when the transmitting transducer S0 and the two receiving sensors S1 and S2 are arranged by the rules in Figure 1, near the liquid level, the echo energy received by two receiving sensors will be changed respectively, because the reflection boundary conditions of the energy circle are changed. The balance of the echo energy between the two receiving sensors can be used to determine the liquid level. 3. Experimental Results 3.1. Measurement System and Initial Conditions The experiment system and the calibration device are shown in Figure 7. In the evaluation of the proposed method, an aluminum container with different wall thickness was used, in which the liquid media was water and the gaseous media was air. The initial conditions and initial values of
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the parameters used in this study are shown in Table 1. In order to simplify the discussion process, the radiuses Sensors 2017, 17,of 706the transmitting transducer and two receiving sensors were chosen as the same value. 7 of 12
(a)
(b)
Figure 7. Measurement system: (a) TX is a transmitting transducer, RX is a receiving sensor; and (b) Figure 7. Measurement system: (a) TX is a transmitting transducer, RX is a receiving sensor; calibration device indevice the experiment. and (b) calibration in the experiment. Table 1. Initial values of the experimental parameters. Table 1. Initial values of the experimental parameters.
Parameters Meaning Parameters the thickness of theMeaning container wall the thicknessofofthe themetal container wall the impedance container the impedance the metal container the impedance of gasofmedia in the container the impedance of gas media in the container the impedance of liquid media in the container the impedance of liquid media in the container the reflection coefficient innerwall walland andgas gas the reflection coefficientbetween between the the inner the reflection coefficient walland andliquid liquid the reflection coefficientbetween between the the inner inner wall the reflection coefficientbetween between the the outer the reflection coefficient outerwall walland andairair center frequency of the transmitting transducer the the center frequency of the transmitting transducer the repetition frequency of a pulse the repetition frequency a pulse the repetition period ofof a pulse the repetition period of a pulse the excitation voltage the operating temperature range of sensors the excitation voltage the diameter of the sensors the operating temperature range of sensors the ultrasonic attenuation coefficient in the container wall. the diameter of the sensors the ultrasonic attenuation coefficient in the container wall. 3.2. Results of Experiment
Initial Values Values L= 8 mm,Initial 25 mm, 40 mm, 50 mm L=Z 8 mm, 25 mm, mm, 50 mm = 17 1040 gm/cm ∙s 2 ·s = 17 × 10510 gm/cm m 0.0004 Z Z= gm/cm ∙s Zg = 0.0004 × 105 gm/cm2 ·s gm/cm ∙ s Z = 1.48 10 Zl = 1.48 × 105 gm/cm2 ·s = 0.99995294 R Rmg = 0.99995294 R = 0.83982683 0.83982683 Rml = Rma = = 0.99995294 0.99995294 fc = 1 MHz f = 1 MHz fr = 100 Hz f = = 0.01 100 Hz T s 0.01 s UT==200 V ◦C (−U10~80) = 200 V r = r1(−10~80) = r2 = 10°C mm α = 2 dB/m
r = r = r = 10 mm α = 2 dB/m
3.2. Results of Experiment 3.2.1. Comparison of Echo Energy under Different Coupling 3.2.1.Figure Comparison ofthe Echo Energy under Different 8 shows measurement results with Coupling the thickness of a container wall being 50 mm. Figure 8a,b shows the change of echo pressure received by the two receiving sensors S1 and S2 Figure 8 shows the measurement results with the thickness of a container wall being 50 mm. with the increase of ∆d from 0 to d under a good coupling and a bad coupling conditions respectively. Figure 8a,b shows the change of echo pressure received by the two receiving sensors S and S From Figure 8a, under good coupling conditions, it can be seen that both of the received energy with the increase of ∆d from 0 to d under a good coupling and a bad coupling conditions of the two sensors S1 and S2 increased with the increase of ∆d from 0 to d, and the two increments respectively. of the sensors S1 and S2 were not equal at the same position with the same ∆d. When ∆d ≥ d and From Figure 8a, under good coupling conditions, it can be seen that both of the received energy ∆d ≤ 0, the state of the two receiving sensors was balance, because the received echo energy of S1 and of the two sensors S and S increased with the increase of ∆d from 0 to d, and the two increments S were equal. of2 the sensors S and S were not equal at the same position with the same ∆d. When ∆d d and Figure 8b shows that both of the echo energy of S1 and S2 significantly fluctuated under bad ∆d ≤ 0, the state of the two receiving sensors was balance, because the received echo energy of S coupling condition at some positions, but it also can be seen that the changing directions of the two and S were equal. Figure 8b shows that both of the echo energy of S and S significantly fluctuated under bad coupling condition at some positions, but it also can be seen that the changing directions of the two energy were consistent: both of them increased or decreased at the same position, because the two receiving sensors had the same coupling characteristic.
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Sensors 2017, 17, 706 8 ofthe 12 two energy were consistent: both of them increased or decreased at the same position, because receiving sensors had the same coupling characteristic. Figure 8c,d shows the difference and ratio of the two echo energy of S and S with the increase Figure 8c,d shows the difference and ratio of the two echo energy of S1 and S2 with the increase of of ∆d from 0 to d under two different conditions respectively. From Figure 8d, it can be seen that ∆d from to dofunder twoecho different conditions From FigureS8d,and it can seen that the ratio the 0ratio the two energy received respectively. by the receiving sensors S be were essentially of thechangeless two echo and energy received by the receiving sensors S and S were essentially changeless and did 2 between the sensors and the wall 1 did not appear to fluctuate, whether the coupling not appear to fluctuate, whether the coupling between the sensors and the wall was good or bad. was good or bad.
Figure 8. The result of two differentcoupling couplingas as the the thickness thickness ofofwall mm, (a) the of of Figure 8. The result of two different wallL=L50 = 50 mm, (a) curves the curves sound pressure of S and S with a good coupling; (b) the curves of sound pressure of S and S sound pressure of S1 and S2 with a good coupling; (b) the curves of sound pressure of S1 and S2 with a bad coupling; (c) the difference of sound pressure of S and S under two different couplings; with a bad coupling; (c) the difference of sound pressure of S1 and S2 under two different couplings; and (d) the ratio of sound pressure of S and S under two different couplings. and (d) the ratio of sound pressure of S1 and S2 under two different couplings.
3.2.2. Results under Two Different Arrangements of Sensors
3.2.2. Results under Two Different Arrangements of Sensors
In Table 2, the data presented are the average values of the results of three times measurements. The symbol h data represents the actual height of the liquidoflevel in a container, is the average In Table 2, the presented are the average values the results of threehtimes measurements. measuring result of the proposed method, and ∆E is the average error. The symbol hl represents the actual height of the liquid level in a container, hm is the average measuring
result of the proposed method, and ∆E is the average error.
Table 2. The result of measurement corresponding to the two arrangement in Figure 1 (mm).
Table 2. The of measurement corresponding to the two arrangement in Figure 1 (mm). L result r1,r2 N d d1 d2 ∆ 50
10
L50
10 r1,r2
50
50 50 50 50 50 50 50 50 50 50 5050 5050 50 50 50
10
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
12.5 12.5 N 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5
12.5 12.5 12.5
61.93 61.93 d 61.93 61.93 61.93 61.93 61.93 61.93 61.93 61.93 61.93 61.93 61.93 61.93 61.93 61.93 61.93
61.93 61.93 61.93
0 0 0 0 0 2r 2r 2r 2r 2r
4r
198.99
d1 5r d2 198.82hm 0 0 0 0 0 2r 2r 2r 2r 2r
6r 4r 8r 5r 10r 6r 2r 8r 3r 10r 4r 2r 6r 3r 8r
4r 6r 8r
198.01 198.99 197.08 198.82 195.52 198.01 198.78 197.08 198.85 195.52 198.14 198.78 197.39 198.85 196.31
198.14 197.39 196.31
200 200 hl 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200
200 200 200
1.02 1.19∆E 1.99 1.02 2.92 1.19 4.49 1.99 1.22 2.92 1.15 4.49 1.86 1.22 2.61 1.15 3.69
1.86 2.61 3.69
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Table 2 shows the measurement results under two different arrangements as described in Figure 1. In the first type of rules, d1 = 0, d2 were taken as 4r, 5r, 6r, 8r, and 10r respectively. In the second type of rules, d1 = 2r, d2 were taken as 2r, 3r, 4r, 6r, and 8r respectively. Figure 9a706corresponds to the first type of rules and shows that the measurement accuracy Sensors 2017, 17, 9 of 12 decreased gradually with the increase of d2 from 4r to 10r. This is because the echo energy received by theTable two receiving sensors gradually reduced with increase of d2 which as resulted in ainreduction 2 shows the measurement results under twothe different arrangements described Figure 1. of Therefore, arrangement, when between S and S is taken as the Inresolution. the first type of rules,indthis = 0, d were taken as the 4r, distance 5r, 6r, 8r,dand 10r respectively. In the second 2 2 1 minimum value optimal. type of rules, d 4r, = the 2r, measurement d were takenaccuracy as 2r, 3r,is4r, 6r, and 8r respectively.
Figure9.9.The Themeasuring measuringresults resultsunder undertwo twodifferent differentarrangements. arrangements.(a)(a)d1d==0 0and and Figure d2 d= = ∼ 10)r; ( 4(4~10)r; = 2r and d = (2~8)r; (c) errors. (b) d (b) d1 = 2r and d2 = ( 2 ∼ 8)r; (c) errors.
Figure 9a corresponds to the first type of rules and shows that the measurement accuracy Figure 9b corresponds to the second type of rules in this arrangement, when d2 is taken as the decreased gradually with the increase of d from 4r to 10r. This is because the echo energy received minimum value 2r, the measurement accuracy is not optimal, which is different from the first rule. by the two receiving sensors gradually reduced with the increase of d which resulted in a reduction It can be seen that when the distance between S1 and S2 was taken as a minimum d2 = 2r, the difference of resolution. Therefore, in this arrangement, when the distance d between S and S is taken as of the two energy of S1 and S2 was less than that of d2 = 3r and d2 = 4r as shown in Figure 10c. the minimum value 4r, the measurement accuracy is optimal. Figure 9c shows the errors with the increase of the distance d2 between S1 and S2 under two Figure 9b corresponds to the second type of rules in this arrangement, when d is taken as the different arrangement rules. When d1 = 0, d2 = 4r in the first rule and d1 = 2r, d2 = 3r in the second minimum value 2r, the measurement accuracy is not optimal, which is different from the first rule. arrangement, the measurement accuracy was optimal, reaching about 1mm, which was higher than It can be seen that when the distance between S and S was taken as a minimum d = 2r, the that of the method in literatures [1,2]. In addition, compared with the methods mentioned in the difference of the two energy of S and S was less than that of d = 3r and d = 4r as shown in introduction, the proposed method has higher stability and reliability. Figure 10c. The uncertainty of the proposed method was the difference of ultrasonic impedance between gas Figure 9c shows the errors with the increase of the distance d between S and S under two and liquid in containers. If this difference is so small that two parts of echo energy are quite similar to different arrangement rules. When d = 0, d = 4r in the first rule and d = 2r, d = 3r in the each other, as the sensors are, respectively, above and below the liquid level, and the measurement second arrangement, the measurement accuracy was optimal, reaching about 1mm, which was will not be possible. higher than that of the method in literatures [1] and [2]. In addition, compared with the methods mentioned in the introduction, the proposed method has higher stability and reliability. The uncertainty of the proposed method was the difference of ultrasonic impedance between gas and liquid in containers. If this difference is so small that two parts of echo energy are quite similar to each other, as the sensors are, respectively, above and below the liquid level, and the measurement will not be possible.
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Figure 10. 10.The The difference of sound andtwo S different under arrangements. two different Figure difference and and ratio ratio of sound pressurepressure of S1 andofS2 Sunder = (4~10)r; d = 2r, d = (2~8)r. arrangements. (a,b) d1 = 0, d2 (a,b) = ( 4 d∼ = 100, d1 = 2r, d(c,d) )r;d(c,d) 2 = ( 2 ∼ 8)r.
Figure 10a,b show the difference and ratio of the echo energy of S and S change with the Figure 10a,b show the difference and ratio of the echo energy of S1 and S2 change with the increase increase d from 4r to 10r, in the first type of arrangement with a good coupling. From them, it can d2 from 4r to 10r, in the first type of arrangement with a good coupling. From them, it can be seen that be seen that the curve values of the difference become smaller, the ratio becomes bigger with the the curve values of the difference become smaller, the ratio becomes bigger with the increase of d2 , increase of d , and the detection resolution reduced gradually. and the detection resolution reduced gradually. Figure 10c,d shows the difference and ratio of the echo energy of S and S change with the Figure 10c,d shows the difference and ratio of the echo energy of S1 and S2 change with the increase d from 2r to 8r, in the second type of arrangement with a good coupling. From Figure 10c, increase d2 from 2r to 8r, in the second type of arrangement with a good coupling. From Figure 10c, it can be seen that the values of the difference was the maximum when d = 3r rather than d = 2r. it can be seen that the values of the difference was the maximum when d2 = 3r rather than d2 = 2r. when d > 4r, the difference decreased with the increase of d . From Figure 10d, it can be seen that when d2 > 4r, the difference decreased with the increase of d2 . From Figure 10d, it can be seen that the the curve values of the ratio became bigger with the increase of d . curve values of the ratio became bigger with the increase of d2 . 4. Discussion 4. Discussion According to this study, the detection results are affected by the rules of sensors arrangement, According to this study, the detection results are affected by the rules of sensors arrangement, which is determined by the values of d and d . Another important influence factor is the thickness which is determined by the values of d1 and d2 . Another important influence factor is the thickness L L of the container wall, which is similar to d . From experimental result, it can be known that with of the container wall, which is similar to d2 . From experimental result, it can be known that with the the increase of the thickness L, the echo energy received by two receiving sensors will decrease and increase of the thickness L, the echo energy received by two receiving sensors will decrease and cause cause a reduction in measurement resolution. On the other hand, if increasing the incident frequency a reduction in measurement resolution. On the other hand, if increasing the incident frequency or the or the size of the transmitting sensor, the accuracy problem caused by the increase of the thickness of size of the transmitting sensor, the accuracy problem caused by the increase of the thickness of the the wall can be improved. wall can be improved. In this study, two kinds of special arrangement rules are used in the experiment, and their In this study, two kinds of special arrangement rules are used in the experiment, and their measurement results are discussed under different coupling conditions. In actual detection, measurement results are discussed under different coupling conditions. In actual detection, according to the different detection environment and initial conditions, the optimal sensors can be according to the different detection environment and initial conditions, the optimal sensors can combined by the arrangement rules and requirements as shown in Figure 1. be combined by the arrangement rules and requirements as shown in Figure 1.
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5. Conclusions The experimental results show that the proposed method is an effective and nondestructive ultrasonic method for liquid level measurement, which has higher detection accuracy, reliability and stability, and has higher practical value. The proposed method reduces the coupling requirements between the sensors and the container wall, which makes it unnecessary for the energy of incident beam to be maintained in a very stable state during the whole detection process. Therefore, the operation of the proposed method is more convenient and flexible, the detection process is more easily controlled, and the measurement results are more reliable, stable, and accurate than the previously developed methods mentioned in the introduction. Acknowledgments: This work was supported by the internal research founding of the North University of China. The authors would like to thank the technical staff in our library for their valuable suggestions to this project. Author Contributions: The work presented in this paper was a collaboration of all authors. Bin Zhang, Yue-Juan Wei, Wen-Yi Liu, Yan-Jun Zhang, and Ji-Jun Xiong designed and established the theoretical model of ultrasonic liquid level detection; Bin Zhang and Yue-Juan Wei conceived and designed the experiments; Bin Zhang, Yue-Juan Wei, and Zong Yao performed the experiments; Liang Zhang improved and debugged the circuit; Bin Zhang and Zong Yao analyzed the data; Bin Zhang wrote the paper, which was discussed and revised by all authors. Conflicts of Interest: The authors declare no conflict of interest.
References 1.
2.
3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
Zhang, B.; Wei, Y.-J.; Liu, W.-Y.; Zhang, Y.-J.; Yao, Z.; Zhao, L.-H.; Xiong, J.-J. A Liquid Level Measurement Technique outside a Sealed Metal Container Based on Ultrasonic Impedance and Echo Energy. Sensors 2017, 17, 185. [CrossRef] [PubMed] Hao, H.H.; Xiong, J.Q. A Method of Liquid Level Measurement Based on Ultrasonic Echo Characteristics. In Proceedings of the 2010 International Conference on Computer Application and System Modeling (ICCASM 2010), Taiyuan, China, 22–24 October 2010. McCulloch, R.W. Measurement of liquid level in demanding environments using thermal differential technology. Proc. Adv. Instrum. 1990, 45, 1859–1867. He, X.P.; Zhang, F.; Li, B.; Zhang, D. The calculation of the echo energy transmission coefficient in ultrasonic liquid level testing. J. Shaanxi Norm. Univ. 2008, 36, 49. Sakharova, V.E.; Kuznetsova, S.A.; Zaitsevb, B.D.; Kuznetsovab, I.E.; Josh, S.G. Liquid level sensor using ultrasonic Lamb waves. Ultrasonics 2003, 41, 319–322. [CrossRef] Joshi, S.G.; Jin, Y. Propagation of ultrasonic Lamb waves in piezoelectric plates. J. Appl. Phys. 1991, 70, 4113–4120. [CrossRef] Schmerr, L.W. Fundamentals of Ultrasonic Nondestructive Evaluation: A Modeling Approach; Plenum Press: New York, NY, USA, 1998. Schmerr, L.W.; Sedov, A. An Elastodynamic Model for Compressional and Shear Wave Transducers. J. Acoust. Soc. Am. 1989, 86, 1988–1999. [CrossRef] Vezzeti, D.J. Propagation of Bounded Ultrasonic Beams in Anisotropic Media. J. Acoust. Soc. Am. 1985, 78, 1103–1108. [CrossRef] Roa-Prada, S.; Scarton, H.A.; Saulnier, G.J.; Shoudy, D.A.; Ashdown, J.D.; Das, P.K.; Gavens, A.J. An Ultrasonic Through-Wall Communication (UTWC) System Model. J. Vibr. Acoust. 2013, 135. [CrossRef] Jeong, H.; Schmerr, L.W., Jr. Ultrasonic Beam Propagation in Highly Anisotropic Materials Simulated by Multi-Gaussian Beams. J. Mech. Sci. Technol. 2007, 21, 1184–1190. [CrossRef] Kim, H.-J.; Park, J.-S.; Song, S.-J. Modeling Angle Beam Ultrasonic Testing Using Multi-Gaussian Beams. J. Nondestruct. Eval. 2004, 23, 81–93. [CrossRef] Spies, M. Ultrasonic field modeling for immersed components using Gaussian beam superposition. Ultrasonics 2007, 46, 138–147. [CrossRef] [PubMed] Bass, R. Diffractions Effects in the Ultrasonic Field of a Piston Source. J. Acoust. Soc. Am. 1958, 30, 602–605. [CrossRef]
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15. 16. 17.
12 of 12
Eaton, D.W. Backscattering from spherical elastic inclusions and accuracy of the kirchhoff approximation for curved interfaces. Geophys. J. Int. 2006, 166, 1249–1258. [CrossRef] Hargreaves, J.A.; Lam, Y.W. An energy interpretation of the Kirchhoff-Helmholtz boundary integral equation and its application to sound field synthesis. Acta Acust. Unit. Acust. 2014, 100, 912–920. [CrossRef] Kohei, Y.; Yasuhiro, O. Optically visualized sound field reconstruction using Kirchhoff-Helmholtz equation. Acoust. Sci. Technol. 2015, 36, 351–354. © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
A Novel Ultrasonic Method for Liquid Level Measurement Based on the Balance of Echo Energy Bin Zhang 1,2 , Yue-Juan Wei 3 , Wen-Yi Liu 1,2, *, Yan-Jun Zhang 1,2, *, Zong Yao 1,2 , Liang Zhang 1,2 and Ji-Jun Xiong 1,2 1
2 3
*
Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China; [email protected] (B.Z.); [email protected] (Z.Y.); [email protected] (L.Z.); [email protected] (J.-J.X.) Science and Technology on Electronic Test & Measurement Laboratory, North University of China, Taiyuan 030051, China Software School of North University of China, Taiyuan 030051, China; [email protected] Correspondence: [email protected] (W.-Y.L.); [email protected] (Y.-J.Z.); Tel.: +86-351-3557-385 (W.-Y.L. & Y.-J.Z.)
Academic Editor: Xiaoning Jiang Received: 13 February 2017; Accepted: 24 March 2017; Published: 28 March 2017
Abstract: This study presents a novel method for determining the liquid level from the outside of a sealed container, which is based on the balance of echo energy received by two receiving sensors. The proposed method uses one transmitting transducer and two receiving sensors that are encapsulated in a coupling plane and arranged by certain rules. The calculation and comparison of echo energy are grounded on the difference ultrasonic impedance between gas and liquid media. First, by analyzing the propagation and attenuation characteristics of ultrasonic waves in a solid, an acoustic model for calculating the echo energy is established and simulated in MATLAB. Second, the proposed method is evaluated through a series of experiments. The difference and ratio of echo energy received by two receiving sensors are calculated and compared under two different coupling conditions. Two kinds of the sensors that are arranged by different rules are selected for measuring the liquid level, and the measurement are analyzed and discussed in detail. Finally, the experimental results indicate that the proposed method can meet the proposed accuracy requirements and can effectively solve the problems caused by some poor coupling conditions. Keywords: ultrasonic impedance; balance; echo energy; coupling; matching layer
1. Introduction In fields such as petroleum, chemical, and aerospace, the real-time monitoring and accurate measurement of the liquid level in a sealed container are important for the industrial automation and safety production [1,2]. In actual industrial production, an appropriate measurement method should be selected to suit the specific environment and safety requirements [3,4]. There are several traditional liquid level measurement methods [1–6], of which the technologies are stable and reliable and the measurement results are accurate. However, these methods usually require some sensors or all of detection equipment to be installed inside a container in advance. Some special industries require a container to be stored with high temperature, high pressure, inflammable, explosive, highly corrosive, or strong, volatile liquid inside. It is easy for a leakage accident to occur, and after a containment failure, maintenance is difficult and costly. For these reasons, some scholars and institutions in the United States began in the 1980s to study and use new technologies based on fiber optics, ultrasound, lasers, and gamma rays for liquid level measurement. Among these, ultrasonic detection technology can achieve a true sense of non-contact Sensors 2017, 17, 706; doi:10.3390/s17040706
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container. Therefore, ultrasonic technology for liquid level detection has been developed rapidly in and non-immersion measurement without damaging the physical structure and integrity of a container. recent years. Therefore, ultrasonic technology for liquid level detection hason been developed rapidly can in recent years. Generally, the liquid level measurement methods based ultrasonic technology be divided Generally, the liquid level methodsas based on ultrasonic technology be divided into four types according to themeasurement realization principle, described in literature [1]. Allcan of them have into four of types according to theand realization described in literature [1]. All of them strengths ultrasonic detection applyingprinciple, conditions.asThey also have some weaknesses, such as have strengths of ultrasonic detection and applying conditions. They also have some weaknesses, high coupling requirements between sensors and the surface of the container wall. In actual such as high coupling requirements between surface of the container wall. In of actual measurement, an appropriate coupling agentsensors shouldand be the chosen according to the material the measurement, an appropriate agentlayer should be chosen according to thetomaterial of the container, and the thickness ofcoupling the coupling should be adjusted according experimental container, the coupling layer are should be adjusted according to measuring experimental results results so and thatthe thethickness incidentofultrasound waves consistent throughout the process, so that the waves areliquid consistent throughout thethe measuring process, because the because theincident premiseultrasound is to determine the level by comparing impedance characteristics of premise positions. is to determine the liquid level by comparing the impedance characteristics of different different Otherwise, the measuring result is inaccurate or meaningless. positions. the measuring result is inaccurate or meaningless. WhenOtherwise, a beam of ultrasound is transmitted from above and below the liquid level respectively, When a beam echo of ultrasound transmitted fromdifferent above and below the liquid level respectively, the two reflected energies isare significantly because of the different ultrasonic the two reflected echo energies are significantly different because of the different ultrasonic impedance impedance between gas and liquid media in a container. This study presents a novel measurement betweenThe gasproposed and liquid mediauses in athe container. This study presents a novel measurement method. method. method balance of echo energy received by two sensors to determine Theliquid proposed method usesoutside the balance echo energy received two sensors to determine the level from the of a of sealed container. It canbysolve the problems causedthebyliquid bad level frombetween the outside of a sealed container. It can solve problems by bad and coupling between coupling sensors and the container wall, andthe can enhancecaused the stability reliability of sensors and the container wall, and can enhance the stability and reliability of measurement. measurement. In the the proposed proposed method, method, three three round round plate plate ultrasonic ultrasonic sensors sensors are are used used and and arranged arranged as as shown shown In Figure 1, 1, and and meet meet the the following following conditions: Figure
Figure d = r +r . Figure1.1.The Thearrangement arrangementrules rulesof ofthree threesensors: sensors: (a) (a) dd1 = = 0; 0; and and (b) (b) d 1 = r1 + r2 .
• • • •
The transducer S is used as an ultrasonic transmitter. The other two sensors, S and S , are The transducer S is used as an ultrasonic transmitter. The other two sensors, S1 and S2 , are used used as receivers; 0 as receivers; The distances d and d meet the conditions 0 ≤ d ≤ r + r , 2r ≤ d ≤ (4r + 2r ). The two The distances d and d meet the conditions 0 ≤ d1 ≤ r1 + r2 , 2r2 ≤ d2 ≤ (4r1 + 2r2 ). The two receiving sensors1 S and2 S are arranged symmetrically along the horizontal coordinate axis; receiving sensors S1 and S2 are arranged symmetrically along the horizontal coordinate axis; Three sensors are placed on the same coupling plane and encapsulated in a rectangular plastic Three sensors box with epoxy;are placed on the same coupling plane and encapsulated in a rectangular plastic box with epoxy;process, the sensors are moved along the longitudinal direction on the surface of In the detection the detection aIn container wall. process, the sensors are moved along the longitudinal direction on the surface of a container wall.
Measuring principle: As shown in Figure 2, when using the transducer S to emit a beam of Measuring principle: As shown in Figure 2, when using the transducer S0 to emit a beam of ultrasonic waves perpendicularly to the outer surface of a container wall, both of the receiving ultrasonic waves perpendicularly to the outer surface of a container wall, both of the receiving sensors sensors S and S could detect echoes reflected by the inner surface if the wall thickness L is less S1 and S2 could detect echoes reflected by the inner surface if the wall thickness L is less than the than the length of the sound field. Because they are geometrically symmetrical to the transmitting length of the sound field. Because they are geometrically symmetrical to the transmitting transducer transducer S , if the reflection boundary conditions at the inner surface are consistent, the echo S0 , if the reflection boundary conditions at the inner surface are consistent, the echo energy received by energy received by the two receiving sensors should be equal in magnitude. The different ultrasonic the two receiving sensors should be equal in magnitude. The different ultrasonic impedance between impedance between the gas and liquid media will make the reflection and transmission of sound the gas and liquid media will make the reflection and transmission of sound waves different at the waves different at the inner surface. Therefore, the acoustic boundary conditions will be changed
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Sensors 2017, 17, 706 3 of 12 inner surface. Therefore, the acoustic boundary conditions will be changed continuously when the continuously when theStransmitting transducer S is moved near the liquid level, and the balance of transmitting transducer is moved near the liquid level, and the balance of echo energy received by 0 continuously when the transmitting transducer S is moved near the liquid level, and the balance of echo energy received by the two receiving sensors S and S will be destroyed. In this research, the the two receiving sensors S1 and S2 will be destroyed. In this research, the balance is used to determine echo energy received by the two receiving sensors S and S will be destroyed. In this research, the balance is used to determine the liquid level. thebalance liquid level. is used to determine the liquid level.
Figure 2.2.The proposed method. method. Figure Themeasuring measuringprinciple principle of of the proposed Figure 2. The measuring principle of the proposed method.
Advantages: In the proposed method, the two receiving sensors are arranged along the same Advantages: receivingsensors sensorsare arearranged arrangedalong along same Advantages:InInthe theproposed proposed method, method, the the two two receiving thethe same coupling plane, and the balance of echo energy received by the two receiving sensors is the only thing coupling plane, and the by the thetwo tworeceiving receivingsensors sensorsisis the only thing coupling plane, and thebalance balanceofofecho echoenergy energy received by the only thing that needs attention. In other words, the ratio of two received echo energy at the same position is that needs attention. In other words, the ratio of two received echo energy at the same position is that needs attention. In other words, the ratio of two received echo energy at the same positionwhat is what we care about, rather than the magnitude of echo energy value. The proposed method reduces wewhat care we about, magnitude of echo energy value. TheThe proposed method reduces care rather about, than ratherthe than the magnitude of echo energy value. proposed method reducesthe the coupling requirements of transmitting sensor, and enhances the reliability, stability, and the coupling requirements of transmitting and enhances the reliability, and coupling requirements of transmitting sensor,sensor, and enhances the reliability, stability,stability, and sensitivity sensitivity of detection. sensitivity of detection. of detection. 2. Theory and Methods 2. Theory and Methods 2. Theory and Methods 2.1. The Energy Circle 2.1.2.1. The Energy Circle The Energy Circle According to the model and measurement of Schmerr [7,8], the sound field of a round piston Accordingtotothe themodel modeland andmeasurement measurement of Schmerr piston According Schmerr[7,8], [7,8],the thesound soundfield fieldofofa around round piston sensor in a solid medium has two different parts [9,10]. In the near field, the beam can maintain a sensor in a solid mediumhas hastwo twodifferent different parts parts [9,10]. In the near field, the beam can maintain a sensor in a solid medium In the near field, the beam can maintain cylindrical shape to transmit because of its smaller divergence angle. In the far field region, the beam a cylindrical shape to transmit because of its smaller divergence angle. In the far field region, the beam cylindrical shape because ofangle, its smaller divergence In the far field region, the beam propagates withtoatransmit certain divergence as shown in Figureangle. 3. propagates with a certaindivergence divergenceangle, angle,as asshown shown in in Figure Figure 3. propagates with a certain 3.
Figure 3. The sound field of a 1 MHz, 20 mm diameter round piston transducer in an aluminum alloy Figure The soundfield fieldofofaa11MHz, MHz, 20 20 mm mm diameter diameter round anan aluminum alloy Figure 3. 3. The sound roundpiston pistontransducer transducerinin aluminum alloy as calculated with a Multi-Gaussian Beam Model. as calculated with a Multi-Gaussian Beam Model. as calculated with a Multi-Gaussian Beam Model.
The sound field was calculated by using Multi-Gaussian Beam Model [11–13], which can The sound field was calculated by using Multi-Gaussian Beam Model [11–13], which can simulate the sound field of a transducer in 2D and 3D. The ultrasonic wave frequency was 1 MHz, The sound fieldfield wasof calculated by in using Multi-Gaussian Beam Model [11–13], simulate the sound a transducer 2D and 3D. The ultrasonic wave frequency waswhich 1 MHz,can the diameter of the transducer was 20 mm, the wall material was aluminum, in which the simulate the sound field of a transducer in 2D and 3D. The ultrasonic wave frequency was the diameter of the transducer was 20 mm, the wall material was aluminum, in which1 MHz, the compressional wave speed was 6300 m/s, the shear wave speed was 3100 m/s, and the ultrasonic compressional wave speed was 6300 m/s, the shear wave speed was 3100 m/s, and the ultrasonic
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the diameter the transducer was 20 mm, the wall material was aluminum, in which the compressional Sensors 2017, 17,of 706 4 of 12 wave speed was 6300 m/s, the shear wave speed was 3100 m/s, and the ultrasonic impedance 5 gm/cm2 ·5s. The 2length of the near field N and the diffusion angle β are given by was 17 × 10was impedance 17 × 10 gm/cm ·s. The length of the near field N and the diffusion angle β are given Equations (1) and (2),(2), respectively [14].[14]. by Equations (1) and respectively r2 N= r (1) (1) N = λc λ 1.22λc (2) β = arcsin 1.22λ (2) β = arcsin 2r 2r where λc is the wavelength of ultrasonic waves in a metal wall, r is the radius of the sensor. the wavelength ultrasonic in a metalbeam wall, will r is the radius of theregion sensor.on inner where λ isFigure From 3, it can beofinferred thatwaves the ultrasonic form a circular From Figure 3, it can be inferred that the ultrasonic beam will form a circular region on inner surface of a container wall after a propagating distance, and the beam energy is mainly concentrated surface of a container wall after a propagating distance, and the beam energy is mainly concentrated in this region. The projected circular region is referred to as the energy circle, of which the diameter is in this region. circular region is referred expressed by dThe andprojected can be calculated by Equation (3): to as the energy circle, of which the diameter is expressed by d and can be calculated by Equation (3): ( dd= L≤ = 2r 2r((L ≤N N)) (3) (3) d d==22[r − N tan L > N) N) [r ++(L ) (L − N) tanββ]] ((L 2.2. Sound Pressure Distribution at Any Point outside the Axis 2.2. Sound Pressure Distribution at Any Point outside the Axis As shown in Figure 4, P(x, y, z) is a point outside the axis of the round piston sensor, the distance As shown in Figure 4, P(x, y, z) is a point outside the axis of the round piston sensor, the distance from the center O(0, 0, 0) of the sensor to the point P(x, y, z) is marked by R = D(O, P). The angle from the center O(0,0,0) of the sensor to the point P(x, y, z) is marked by R = D(O, P). The angle between R and the x-axis is denoted by θ. Then, according to the Kirchhoff integral theorem [15–17], between R and the x-axis is denoted by θ. Then, according to the Kirchhoff integral theorem [15– the sound pressure at the point P can be calculated as 17], the sound pressure at the point P can be calculated as 2 πa 2J1(kasinθ) (kasinθ) πa 2J p(p(R, R, θθ) = (4) ) = ∙ ·pp0 (4) λR kasinθ λR kasinθ
theinitial initialsound soundpressure pressure sound source, is the wavelength of ultrasonic waves where pp0 isisthe where ofof thethe sound source, λ isλthe wavelength of ultrasonic waves in a in a medium, a radius is the radius of the and sensor, k is the waveJ1number; J kind is theoffirst first medium, a is the of the sensor, k is and the wave number; is the first first kind orderof Bessel order Bessel The geometric meaning of other variables is shown function. Thefunction. geometric meaning of other variables is shown in Figure 4. in Figure 4.
4. Calculating Calculatingthe theacoustic acoustic field characteristics a round transducer at anyoutside point Figure 4. field characteristics of a of round pistonpiston transducer at any point outside axis according to the Kirchhoff integral theorem. the axis the according to the Kirchhoff integral theorem.
Because of the interference interference in the near near field field of of aa round round piston piston transducer, transducer, Equation Equation (4) (4) is is valid valid Because of the in the only in in the the far far field, field, which which requires requires the the wall wall thickness thickness to meet the condition LL > only to meet the condition > NN in in aa detection. detection. This requirement can be achieved by adjusting the near field length N for a given container. This requirement can be achieved by adjusting the near field length N for a given container. Equation (1) Equation (1) demonstrates that the radius of the transducer and the ultrasound wave length in a demonstrates that the radius of the transducer and the ultrasound wave length in a container wall are container wall are critical factors, and the latter is associated with the transmitting frequency and the critical factors, and the latter is associated with the transmitting frequency and the wall material. wall material. 2.3. Analysis of Echo Energy According to the basic knowledge of acoustics, ultrasonic waves will be refracted and reflected at an interface with discontinuous impedance, which follows the refraction and reflection principle of sound waves.
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2.3. Analysis of Echo Energy According to the basic knowledge of acoustics, ultrasonic waves will be refracted and reflected at an interface with Sensors 2017, 17, 706 discontinuous impedance, which follows the refraction and reflection principle 5 ofof 12 sound waves. As shown in Figure 5, when the transmitting transducer S0 is excited to transmit an ultrasonic beam into the wall, part of the ultrasonic beam will be reflected by the interface 2, and the echoes will be oscillated repeatedly between interfaces 1 and 2 until they decay to zero. Another part of the beam will transmit into the gas-liquid medium in container, of which the energy may decay to zero in propagating process, or may penetrate the gas-liquid medium and be reflected by interfaces 3 and 4. All of these reflected echoes can be detected by the two receiving sensors S1 and S2 that are attached to Sensors 2017, 17, 706 5 of 12 the outer surface of the container wall.
Figure 5. The process of an ultrasonic beam propagating in a container. S is a transmitter, S and S are two receivers, 1,2,3,4 represent the four interfaces of the container.
As shown in Figure 5, when the transmitting transducer S is excited to transmit an ultrasonic beam into the wall, part of the ultrasonic beam will be reflected by the interface 2, and the echoes will be oscillated repeatedly between interfaces 1 and 2 until they decay to zero. Another part of the beam will transmit into the gas-liquid medium in container, of which the energy may decay to zero in propagating process, or of may penetratebeam the gas-liquid medium and beSreflected by interfaces Figure 5. The process an ultrasonic propagating in a container. is a transmitter, S and 3S2and 4. Figure 5. The process of an ultrasonic beam propagating in a container. 0S is a transmitter,1 S and All of these reflected echoes can be detected by the two receiving sensors S and S that are attached are two receivers, 1,2,3,4 represent the four interfaces of the container. S are two receivers, 1,2,3,4 represent the four interfaces of the container. to the outer surface of the container wall. Asshown shown inFigure Figure6,6,in inthe thedetection detectionprocess, process,when whenthe thetop topof ofthe theenergy energycircle circleexceeds exceedsthe the As in Figure 5, when the transmitting transducer S is excited to transmit an ultrasonic liquid level, the exceeding height is represented by ∆d and 0 ≤ ∆d ≤ d. Assuming that the total area liquid level, the exceeding is represented by ∆d and 0 ≤ by ∆d the ≤ d. Assuming thatthe theechoes total area beam into the wall, part of height the ultrasonic beam will be reflected interface 2, and will of the energy circle is A, the area of the energy circle above the liquid level is denoted by A andlet let of energyrepeatedly circle is A, between the area interfaces of the energy circle above liquid denoted by of ATthe , ,and bethe oscillated 1 and 2 until theythe decay to level zero. is Another part beam ⁄ r = A A . rwill transmit into the gas-liquid medium in container, of which the energy may decay to zero in s =A T /A. propagating process, or may penetrate the gas-liquid medium and be reflected by interfaces 3 and 4. All of these reflected echoes can be detected by the two receiving sensors S and S that are attached to the outer surface of the container wall. As shown in Figure 6, in the detection process, when the top of the energy circle exceeds the liquid level, the exceeding height is represented by ∆d and 0 ≤ ∆d ≤ d. Assuming that the total area of the energy circle is A, the area of the energy circle above the liquid level is denoted by A , and let r = A ⁄A.
Figure Figure 6. 6. Calculating Calculating the the echo echo energy energy received received by by the the two two receiving receiving sensors sensors SS1 and andS2S. .
In Figure 6, when taking ρ = d/2 and 0 ≤ φ ≤ π, we can get the value of ∆d and the ratio r by Equations (5) and (6). d ∆d = (1 − cos φ) 2 1 r = (φ − sin φ cos φ) Figure 6. Calculating the echo energyπreceived by the two receiving sensors S and S .
(5) (6)
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In Figure 6, when taking ρ = d/2 and 0 ≤ ϕ ≤ π, we can get the value of ∆d and the ratio rs by Equations (5) and (6). d (1 − cos ϕ) 2
(5)
1 (ϕ − sin ϕ cos ϕ) π
(6)
∆d = rs =
When 0 ≤ ∆d ≤ d, the energy circle is divided into two parts by the liquid level, which makes the acoustic boundary conditions of the two parts different. When an ultrasonic beam propagates first to interface 2, the sound pressure in two parts of energy circle are represented by Pg and Pl receptively, and assuming Pg > Pl , as shown in Figure 6. Here, the energy circle can be approximately regarded as a round transmitting transducer. Assuming that there is a point P(ρ, ϕ) in the upper part of the energy circle, and with the energy circle moving up, the average sound pressure at the point P increases from Pl to Pg . According to Equation (4), the sound pressure of the two receiving sensors S1 and S2 can be obtained by integrating all the points in the red part of the energy circle, which can be described approximately by Equations (7) and (8) ∆ps1 (h1, θ) =
π(d/2)2 ·rs λh1
!
∆ps2 (h2, θ) =
π(d/2)2 ·rs λh2
!
2J1 (k(d/2) sin θ) · pg − pl ·πr22 k(d/2) sin θ
(7)
2J1 (k(d/2) sin θ) · pg − pl ·πr22 k(d/2) sin θ
(8)
where ρ is the polar radius, ϕ is the polar angle, θ is the angle between R1 (or R2) and the x-axis, h1 = D(P, S1 ), h2 = D(P, S2 ), R1 = D(O, S1 ) = h21 + ρ2 − 2 sin θ cos ϕ, R2 = D(O, S2 ) = h22 + ρ2 − 2 sin θ cos ϕ, Pg = P0 e−αL Rmg and Pl = P0 e−αL Rml , Rmg represents the reflection coefficient at the upper part of the energy circle, Rml represents the reflection coefficient at the lower part of the energy circle. Furthermore, it is assumed that the echo energy in the wall will decay to a very small amount after n times, which can be negligible relative to the total energy received by receiving sensor. Therefore, when the sound beam is reflected to the outer surface of the wall at the n times, the total pressure of S1 and S2 can be derived as following equations: ∑ ps1 (h1, θ) = ∑ ps2 (h2, θ) =
π( d2 ) λh1
π(d/2)2 λh2
2
h
h
2J1 (k(d/2) sin θ) k(d/2) sin θ
2J1 (k(d/2) sin θ) k(d/2) sin θ
i
i
n n −1 −2iαL −1 −2iαL e + (1 − rs )· ∑ Riml Rima e ·P0 ·πr22 · rs · ∑ Rimg Rima i=1
n n −1 −2iαL −1 −2iαL e e + (1 − rs )· ∑ Riml Rima ·P0 ·πr22 · rs · ∑ Rimg Rima i=1
(9)
i=1
(10)
i=1
where Rma represents the reflection coefficient at interface 1, α is the attenuation coefficient of a container, and L is the thickness of a container wall. In conclusion, when the transmitting transducer S0 and the two receiving sensors S1 and S2 are arranged by the rules in Figure 1, near the liquid level, the echo energy received by two receiving sensors will be changed respectively, because the reflection boundary conditions of the energy circle are changed. The balance of the echo energy between the two receiving sensors can be used to determine the liquid level. 3. Experimental Results 3.1. Measurement System and Initial Conditions The experiment system and the calibration device are shown in Figure 7. In the evaluation of the proposed method, an aluminum container with different wall thickness was used, in which the liquid media was water and the gaseous media was air. The initial conditions and initial values of
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the parameters used in this study are shown in Table 1. In order to simplify the discussion process, the radiuses Sensors 2017, 17,of 706the transmitting transducer and two receiving sensors were chosen as the same value. 7 of 12
(a)
(b)
Figure 7. Measurement system: (a) TX is a transmitting transducer, RX is a receiving sensor; and (b) Figure 7. Measurement system: (a) TX is a transmitting transducer, RX is a receiving sensor; calibration device indevice the experiment. and (b) calibration in the experiment. Table 1. Initial values of the experimental parameters. Table 1. Initial values of the experimental parameters.
Parameters Meaning Parameters the thickness of theMeaning container wall the thicknessofofthe themetal container wall the impedance container the impedance the metal container the impedance of gasofmedia in the container the impedance of gas media in the container the impedance of liquid media in the container the impedance of liquid media in the container the reflection coefficient innerwall walland andgas gas the reflection coefficientbetween between the the inner the reflection coefficient walland andliquid liquid the reflection coefficientbetween between the the inner inner wall the reflection coefficientbetween between the the outer the reflection coefficient outerwall walland andairair center frequency of the transmitting transducer the the center frequency of the transmitting transducer the repetition frequency of a pulse the repetition frequency a pulse the repetition period ofof a pulse the repetition period of a pulse the excitation voltage the operating temperature range of sensors the excitation voltage the diameter of the sensors the operating temperature range of sensors the ultrasonic attenuation coefficient in the container wall. the diameter of the sensors the ultrasonic attenuation coefficient in the container wall. 3.2. Results of Experiment
Initial Values Values L= 8 mm,Initial 25 mm, 40 mm, 50 mm L=Z 8 mm, 25 mm, mm, 50 mm = 17 1040 gm/cm ∙s 2 ·s = 17 × 10510 gm/cm m 0.0004 Z Z= gm/cm ∙s Zg = 0.0004 × 105 gm/cm2 ·s gm/cm ∙ s Z = 1.48 10 Zl = 1.48 × 105 gm/cm2 ·s = 0.99995294 R Rmg = 0.99995294 R = 0.83982683 0.83982683 Rml = Rma = = 0.99995294 0.99995294 fc = 1 MHz f = 1 MHz fr = 100 Hz f = = 0.01 100 Hz T s 0.01 s UT==200 V ◦C (−U10~80) = 200 V r = r1(−10~80) = r2 = 10°C mm α = 2 dB/m
r = r = r = 10 mm α = 2 dB/m
3.2. Results of Experiment 3.2.1. Comparison of Echo Energy under Different Coupling 3.2.1.Figure Comparison ofthe Echo Energy under Different 8 shows measurement results with Coupling the thickness of a container wall being 50 mm. Figure 8a,b shows the change of echo pressure received by the two receiving sensors S1 and S2 Figure 8 shows the measurement results with the thickness of a container wall being 50 mm. with the increase of ∆d from 0 to d under a good coupling and a bad coupling conditions respectively. Figure 8a,b shows the change of echo pressure received by the two receiving sensors S and S From Figure 8a, under good coupling conditions, it can be seen that both of the received energy with the increase of ∆d from 0 to d under a good coupling and a bad coupling conditions of the two sensors S1 and S2 increased with the increase of ∆d from 0 to d, and the two increments respectively. of the sensors S1 and S2 were not equal at the same position with the same ∆d. When ∆d ≥ d and From Figure 8a, under good coupling conditions, it can be seen that both of the received energy ∆d ≤ 0, the state of the two receiving sensors was balance, because the received echo energy of S1 and of the two sensors S and S increased with the increase of ∆d from 0 to d, and the two increments S were equal. of2 the sensors S and S were not equal at the same position with the same ∆d. When ∆d d and Figure 8b shows that both of the echo energy of S1 and S2 significantly fluctuated under bad ∆d ≤ 0, the state of the two receiving sensors was balance, because the received echo energy of S coupling condition at some positions, but it also can be seen that the changing directions of the two and S were equal. Figure 8b shows that both of the echo energy of S and S significantly fluctuated under bad coupling condition at some positions, but it also can be seen that the changing directions of the two energy were consistent: both of them increased or decreased at the same position, because the two receiving sensors had the same coupling characteristic.
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Sensors 2017, 17, 706 8 ofthe 12 two energy were consistent: both of them increased or decreased at the same position, because receiving sensors had the same coupling characteristic. Figure 8c,d shows the difference and ratio of the two echo energy of S and S with the increase Figure 8c,d shows the difference and ratio of the two echo energy of S1 and S2 with the increase of of ∆d from 0 to d under two different conditions respectively. From Figure 8d, it can be seen that ∆d from to dofunder twoecho different conditions From FigureS8d,and it can seen that the ratio the 0ratio the two energy received respectively. by the receiving sensors S be were essentially of thechangeless two echo and energy received by the receiving sensors S and S were essentially changeless and did 2 between the sensors and the wall 1 did not appear to fluctuate, whether the coupling not appear to fluctuate, whether the coupling between the sensors and the wall was good or bad. was good or bad.
Figure 8. The result of two differentcoupling couplingas as the the thickness thickness ofofwall mm, (a) the of of Figure 8. The result of two different wallL=L50 = 50 mm, (a) curves the curves sound pressure of S and S with a good coupling; (b) the curves of sound pressure of S and S sound pressure of S1 and S2 with a good coupling; (b) the curves of sound pressure of S1 and S2 with a bad coupling; (c) the difference of sound pressure of S and S under two different couplings; with a bad coupling; (c) the difference of sound pressure of S1 and S2 under two different couplings; and (d) the ratio of sound pressure of S and S under two different couplings. and (d) the ratio of sound pressure of S1 and S2 under two different couplings.
3.2.2. Results under Two Different Arrangements of Sensors
3.2.2. Results under Two Different Arrangements of Sensors
In Table 2, the data presented are the average values of the results of three times measurements. The symbol h data represents the actual height of the liquidoflevel in a container, is the average In Table 2, the presented are the average values the results of threehtimes measurements. measuring result of the proposed method, and ∆E is the average error. The symbol hl represents the actual height of the liquid level in a container, hm is the average measuring
result of the proposed method, and ∆E is the average error.
Table 2. The result of measurement corresponding to the two arrangement in Figure 1 (mm).
Table 2. The of measurement corresponding to the two arrangement in Figure 1 (mm). L result r1,r2 N d d1 d2 ∆ 50
10
L50
10 r1,r2
50
50 50 50 50 50 50 50 50 50 50 5050 5050 50 50 50
10
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
12.5 12.5 N 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5
12.5 12.5 12.5
61.93 61.93 d 61.93 61.93 61.93 61.93 61.93 61.93 61.93 61.93 61.93 61.93 61.93 61.93 61.93 61.93 61.93
61.93 61.93 61.93
0 0 0 0 0 2r 2r 2r 2r 2r
4r
198.99
d1 5r d2 198.82hm 0 0 0 0 0 2r 2r 2r 2r 2r
6r 4r 8r 5r 10r 6r 2r 8r 3r 10r 4r 2r 6r 3r 8r
4r 6r 8r
198.01 198.99 197.08 198.82 195.52 198.01 198.78 197.08 198.85 195.52 198.14 198.78 197.39 198.85 196.31
198.14 197.39 196.31
200 200 hl 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200
200 200 200
1.02 1.19∆E 1.99 1.02 2.92 1.19 4.49 1.99 1.22 2.92 1.15 4.49 1.86 1.22 2.61 1.15 3.69
1.86 2.61 3.69
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Table 2 shows the measurement results under two different arrangements as described in Figure 1. In the first type of rules, d1 = 0, d2 were taken as 4r, 5r, 6r, 8r, and 10r respectively. In the second type of rules, d1 = 2r, d2 were taken as 2r, 3r, 4r, 6r, and 8r respectively. Figure 9a706corresponds to the first type of rules and shows that the measurement accuracy Sensors 2017, 17, 9 of 12 decreased gradually with the increase of d2 from 4r to 10r. This is because the echo energy received by theTable two receiving sensors gradually reduced with increase of d2 which as resulted in ainreduction 2 shows the measurement results under twothe different arrangements described Figure 1. of Therefore, arrangement, when between S and S is taken as the Inresolution. the first type of rules,indthis = 0, d were taken as the 4r, distance 5r, 6r, 8r,dand 10r respectively. In the second 2 2 1 minimum value optimal. type of rules, d 4r, = the 2r, measurement d were takenaccuracy as 2r, 3r,is4r, 6r, and 8r respectively.
Figure9.9.The Themeasuring measuringresults resultsunder undertwo twodifferent differentarrangements. arrangements.(a)(a)d1d==0 0and and Figure d2 d= = ∼ 10)r; ( 4(4~10)r; = 2r and d = (2~8)r; (c) errors. (b) d (b) d1 = 2r and d2 = ( 2 ∼ 8)r; (c) errors.
Figure 9a corresponds to the first type of rules and shows that the measurement accuracy Figure 9b corresponds to the second type of rules in this arrangement, when d2 is taken as the decreased gradually with the increase of d from 4r to 10r. This is because the echo energy received minimum value 2r, the measurement accuracy is not optimal, which is different from the first rule. by the two receiving sensors gradually reduced with the increase of d which resulted in a reduction It can be seen that when the distance between S1 and S2 was taken as a minimum d2 = 2r, the difference of resolution. Therefore, in this arrangement, when the distance d between S and S is taken as of the two energy of S1 and S2 was less than that of d2 = 3r and d2 = 4r as shown in Figure 10c. the minimum value 4r, the measurement accuracy is optimal. Figure 9c shows the errors with the increase of the distance d2 between S1 and S2 under two Figure 9b corresponds to the second type of rules in this arrangement, when d is taken as the different arrangement rules. When d1 = 0, d2 = 4r in the first rule and d1 = 2r, d2 = 3r in the second minimum value 2r, the measurement accuracy is not optimal, which is different from the first rule. arrangement, the measurement accuracy was optimal, reaching about 1mm, which was higher than It can be seen that when the distance between S and S was taken as a minimum d = 2r, the that of the method in literatures [1,2]. In addition, compared with the methods mentioned in the difference of the two energy of S and S was less than that of d = 3r and d = 4r as shown in introduction, the proposed method has higher stability and reliability. Figure 10c. The uncertainty of the proposed method was the difference of ultrasonic impedance between gas Figure 9c shows the errors with the increase of the distance d between S and S under two and liquid in containers. If this difference is so small that two parts of echo energy are quite similar to different arrangement rules. When d = 0, d = 4r in the first rule and d = 2r, d = 3r in the each other, as the sensors are, respectively, above and below the liquid level, and the measurement second arrangement, the measurement accuracy was optimal, reaching about 1mm, which was will not be possible. higher than that of the method in literatures [1] and [2]. In addition, compared with the methods mentioned in the introduction, the proposed method has higher stability and reliability. The uncertainty of the proposed method was the difference of ultrasonic impedance between gas and liquid in containers. If this difference is so small that two parts of echo energy are quite similar to each other, as the sensors are, respectively, above and below the liquid level, and the measurement will not be possible.
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Figure 10. 10.The The difference of sound andtwo S different under arrangements. two different Figure difference and and ratio ratio of sound pressurepressure of S1 andofS2 Sunder = (4~10)r; d = 2r, d = (2~8)r. arrangements. (a,b) d1 = 0, d2 (a,b) = ( 4 d∼ = 100, d1 = 2r, d(c,d) )r;d(c,d) 2 = ( 2 ∼ 8)r.
Figure 10a,b show the difference and ratio of the echo energy of S and S change with the Figure 10a,b show the difference and ratio of the echo energy of S1 and S2 change with the increase increase d from 4r to 10r, in the first type of arrangement with a good coupling. From them, it can d2 from 4r to 10r, in the first type of arrangement with a good coupling. From them, it can be seen that be seen that the curve values of the difference become smaller, the ratio becomes bigger with the the curve values of the difference become smaller, the ratio becomes bigger with the increase of d2 , increase of d , and the detection resolution reduced gradually. and the detection resolution reduced gradually. Figure 10c,d shows the difference and ratio of the echo energy of S and S change with the Figure 10c,d shows the difference and ratio of the echo energy of S1 and S2 change with the increase d from 2r to 8r, in the second type of arrangement with a good coupling. From Figure 10c, increase d2 from 2r to 8r, in the second type of arrangement with a good coupling. From Figure 10c, it can be seen that the values of the difference was the maximum when d = 3r rather than d = 2r. it can be seen that the values of the difference was the maximum when d2 = 3r rather than d2 = 2r. when d > 4r, the difference decreased with the increase of d . From Figure 10d, it can be seen that when d2 > 4r, the difference decreased with the increase of d2 . From Figure 10d, it can be seen that the the curve values of the ratio became bigger with the increase of d . curve values of the ratio became bigger with the increase of d2 . 4. Discussion 4. Discussion According to this study, the detection results are affected by the rules of sensors arrangement, According to this study, the detection results are affected by the rules of sensors arrangement, which is determined by the values of d and d . Another important influence factor is the thickness which is determined by the values of d1 and d2 . Another important influence factor is the thickness L L of the container wall, which is similar to d . From experimental result, it can be known that with of the container wall, which is similar to d2 . From experimental result, it can be known that with the the increase of the thickness L, the echo energy received by two receiving sensors will decrease and increase of the thickness L, the echo energy received by two receiving sensors will decrease and cause cause a reduction in measurement resolution. On the other hand, if increasing the incident frequency a reduction in measurement resolution. On the other hand, if increasing the incident frequency or the or the size of the transmitting sensor, the accuracy problem caused by the increase of the thickness of size of the transmitting sensor, the accuracy problem caused by the increase of the thickness of the the wall can be improved. wall can be improved. In this study, two kinds of special arrangement rules are used in the experiment, and their In this study, two kinds of special arrangement rules are used in the experiment, and their measurement results are discussed under different coupling conditions. In actual detection, measurement results are discussed under different coupling conditions. In actual detection, according to the different detection environment and initial conditions, the optimal sensors can be according to the different detection environment and initial conditions, the optimal sensors can combined by the arrangement rules and requirements as shown in Figure 1. be combined by the arrangement rules and requirements as shown in Figure 1.
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5. Conclusions The experimental results show that the proposed method is an effective and nondestructive ultrasonic method for liquid level measurement, which has higher detection accuracy, reliability and stability, and has higher practical value. The proposed method reduces the coupling requirements between the sensors and the container wall, which makes it unnecessary for the energy of incident beam to be maintained in a very stable state during the whole detection process. Therefore, the operation of the proposed method is more convenient and flexible, the detection process is more easily controlled, and the measurement results are more reliable, stable, and accurate than the previously developed methods mentioned in the introduction. Acknowledgments: This work was supported by the internal research founding of the North University of China. The authors would like to thank the technical staff in our library for their valuable suggestions to this project. Author Contributions: The work presented in this paper was a collaboration of all authors. Bin Zhang, Yue-Juan Wei, Wen-Yi Liu, Yan-Jun Zhang, and Ji-Jun Xiong designed and established the theoretical model of ultrasonic liquid level detection; Bin Zhang and Yue-Juan Wei conceived and designed the experiments; Bin Zhang, Yue-Juan Wei, and Zong Yao performed the experiments; Liang Zhang improved and debugged the circuit; Bin Zhang and Zong Yao analyzed the data; Bin Zhang wrote the paper, which was discussed and revised by all authors. Conflicts of Interest: The authors declare no conflict of interest.
References 1.
2.
3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
Zhang, B.; Wei, Y.-J.; Liu, W.-Y.; Zhang, Y.-J.; Yao, Z.; Zhao, L.-H.; Xiong, J.-J. A Liquid Level Measurement Technique outside a Sealed Metal Container Based on Ultrasonic Impedance and Echo Energy. Sensors 2017, 17, 185. [CrossRef] [PubMed] Hao, H.H.; Xiong, J.Q. A Method of Liquid Level Measurement Based on Ultrasonic Echo Characteristics. In Proceedings of the 2010 International Conference on Computer Application and System Modeling (ICCASM 2010), Taiyuan, China, 22–24 October 2010. McCulloch, R.W. Measurement of liquid level in demanding environments using thermal differential technology. Proc. Adv. Instrum. 1990, 45, 1859–1867. He, X.P.; Zhang, F.; Li, B.; Zhang, D. The calculation of the echo energy transmission coefficient in ultrasonic liquid level testing. J. Shaanxi Norm. Univ. 2008, 36, 49. Sakharova, V.E.; Kuznetsova, S.A.; Zaitsevb, B.D.; Kuznetsovab, I.E.; Josh, S.G. Liquid level sensor using ultrasonic Lamb waves. Ultrasonics 2003, 41, 319–322. [CrossRef] Joshi, S.G.; Jin, Y. Propagation of ultrasonic Lamb waves in piezoelectric plates. J. Appl. Phys. 1991, 70, 4113–4120. [CrossRef] Schmerr, L.W. Fundamentals of Ultrasonic Nondestructive Evaluation: A Modeling Approach; Plenum Press: New York, NY, USA, 1998. Schmerr, L.W.; Sedov, A. An Elastodynamic Model for Compressional and Shear Wave Transducers. J. Acoust. Soc. Am. 1989, 86, 1988–1999. [CrossRef] Vezzeti, D.J. Propagation of Bounded Ultrasonic Beams in Anisotropic Media. J. Acoust. Soc. Am. 1985, 78, 1103–1108. [CrossRef] Roa-Prada, S.; Scarton, H.A.; Saulnier, G.J.; Shoudy, D.A.; Ashdown, J.D.; Das, P.K.; Gavens, A.J. An Ultrasonic Through-Wall Communication (UTWC) System Model. J. Vibr. Acoust. 2013, 135. [CrossRef] Jeong, H.; Schmerr, L.W., Jr. Ultrasonic Beam Propagation in Highly Anisotropic Materials Simulated by Multi-Gaussian Beams. J. Mech. Sci. Technol. 2007, 21, 1184–1190. [CrossRef] Kim, H.-J.; Park, J.-S.; Song, S.-J. Modeling Angle Beam Ultrasonic Testing Using Multi-Gaussian Beams. J. Nondestruct. Eval. 2004, 23, 81–93. [CrossRef] Spies, M. Ultrasonic field modeling for immersed components using Gaussian beam superposition. Ultrasonics 2007, 46, 138–147. [CrossRef] [PubMed] Bass, R. Diffractions Effects in the Ultrasonic Field of a Piston Source. J. Acoust. Soc. Am. 1958, 30, 602–605. [CrossRef]
Sensors 2017, 17, 706
15. 16. 17.
12 of 12
Eaton, D.W. Backscattering from spherical elastic inclusions and accuracy of the kirchhoff approximation for curved interfaces. Geophys. J. Int. 2006, 166, 1249–1258. [CrossRef] Hargreaves, J.A.; Lam, Y.W. An energy interpretation of the Kirchhoff-Helmholtz boundary integral equation and its application to sound field synthesis. Acta Acust. Unit. Acust. 2014, 100, 912–920. [CrossRef] Kohei, Y.; Yasuhiro, O. Optically visualized sound field reconstruction using Kirchhoff-Helmholtz equation. Acoust. Sci. Technol. 2015, 36, 351–354. © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
