- Email: [email protected]
Ultrasonic characterization of liquids using resonance antireflection
Ultrasonics 38 (2000) 200–205 www.elsevier.nl/locate/ultras
Ultrasonic characterization of liquids using resonance antireflection M. Hirnschrodt a, *, A. v. Jena b, T. Vontz b, B. Fischer b, R. Lerch a a University of Linz, Altenbergerstr. 69, A-4040 Linz, Austria b Siemens AG, ZT KM 2, Otto-Hahn-Ring 6, D-81730 Mu¨nchen, Germany
Abstract This paper presents an ultrasonic method for measuring the density of liquids with a solid layer separating a reference fluid and a test fluid. By adjusting the frequency of the exciting signal according to the thickness of the layer, it is possible to generate destructive interference of the waves reflected at the first and at the second boundary of the layer. Thus, the layer appears to vanish for the incident waves. The resulting echo signal depends only on the acoustic impedances of the reference fluid and the test fluid and the density which is of interest can be extracted. Short and long-term drifts of the electronics and the ultrasonic transducer implied are eliminated by using the well-known pulse–echo technique with additional frontwave detection. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Antireflection; Density; Liquids; Resonance; Ultrasonic
1. Introduction Density is a fundamental parameter for describing a fluid. It is an indicator of the type of fluid, its constituents and any contaminants. In conjunction with volume measurement it gives mass. In process industries, especially in the petrochemical industry, density measurement is used for process control and measurement of mass flow. There is a need for mass flow measurement meters with adequate accuracy (±1%), compact size, easy installation and low costs. These demands are met by the combination of an ultrasonic volume flow sensor with an ultrasonic density sensor. In principle an ultrasound density sensor uses the reflection at discontinuities of acoustic impedance, where the reflection coefficient is relative to the ratio of the acoustic impedance of the adjacent media [1–4]. To establish such a boundary zone, a solid buffer rod can be used, with one side directly coupled with the transducer and the other side with the fluid [5–7]. The difficulty of this approach, however, is the fact that a larger difference in the acoustic impedances between the solid and the liquid results in a lower sensitivity for changes in the density of the fluid. * Corresponding author. Fax: +49-89-636-46881. E-mail address: [email protected] (M. Hirnschrodt)
In this paper, it is shown that this limitation can be overcome by using resonance antireflection ( RAR) with a half-wave layer as a separating wall between the flow tube and the ultrasound sensor, as illustrated in Fig. 1. The frequency of the incident sound wave is adjusted so that the wavelength inside the layer is exactly twice its thickness and complete destructive interference is accomplished. The half-wave layer then acts as an ideal antireflecting coating and the reflected intensity depends only on the difference in the acoustic impedances of the two media in front of and behind the layer (‘virtual boundary’). The reference medium in the ‘pre-run’ chamber can be chosen to achieve the highest sensitivity of the measurement in the most interesting range of densities.
2. Acoustic determination of density using reference principle 2.1. Fundamentals To achieve a small influence of parameters difficult to control, such as aging of materials, transducer longterm variations and drifts in the electronics, the pulse– echo method is used for the measurement of the reflection coefficient. A single ultrasonic transducer acts in the pulse–echo mode sequentially as transmitter and
0041-624X/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S0 0 4 1 -6 2 4 X ( 9 9 ) 0 0 05 0 - 5
M. Hirnschrodt et al. / Ultrasonics 38 (2000) 200–205
201
Fig. 1. Principle of ultrasonic mass flow measurement using time-of-flight measurement for volume flow and resonance antireflection for density.
receiver for ultrasound bursts. The amplitude A of the R reflected front wave depends on the transmitted signal level A and on the acoustic impedances involved at the 0 boundary. With the reflection coefficient given by: A R= R , (1) A 0 the density can be extracted by using the well-known equations Z −Z 1 , Z=rc, R= 2 Z +Z 2 1 which results in c 1+R r =r 1 . 2 1 c 1−R 2
reflection coefficient of a water/ethanol interface. It can be seen that using steel as a reference medium, whose acoustic impedance is 30 times higher that of water, results in a change of the reflection coefficient of about 11%. Using polymethyl methacrylate (PMMA) with an approx. 2 times higher impedance leads to a sensitivity of about 105% and ethanol with a 0.65 times higher impedance results in a 125% change of reflection. With the resonance antireflection method it is possible to use transient and steady state parts of the echo signal
(2)
(3)
2.2. Resonance antireflection method Compared with the method using a solid buffer rod as reference medium the resonance antireflection method shows a higher sensitivity for changes in the density of the test liquid. This results from the better matching of the acoustic impedances by using a liquid reference medium instead of a solid. In Fig. 2 the relative change of the reflection coefficient DR/R for different referRef ence materials as a function of the acoustic impedance of various test fluids is shown, normalized for the
Fig. 2. Variation of reflection coefficient for different reference materials versus acoustic impedance.
202
M. Hirnschrodt et al. / Ultrasonics 38 (2000) 200–205
(see Fig. 5) for the reference measurement and for the interrogation of the separation layer. In Fig. 3(a) the detection of the reference signal is illustrated. Reflection takes place at all interfaces. A∞ is 0 the contribution of the reflection at the interface reference fluid/half-wave layer (Fig. 3(a)) and A is the R reflection from the interface half-wave layer/test fluid (Fig. 3(b)). Since the amplitude A∞ of the received wave 0 front is not influenced by the acoustic properties of the test fluid, it can be used to represent the incident intensity, which is necessary for the calculation of the reflection coefficient. Certainly this is only true for the small time window where the wave, reflected at the boundary Z /Z , has not yet reached the first boundary 2 3 and therefore has not yet affected the incident wave. Thus only the very first leading edge oscillations are suitable for determining the reference intensity. In the steady state condition, waves reflected at the Z /Z and 1 2 the Z /Z boundaries do interfere with each other. 2 3 Because of the sign reversal at the second interface and the precise frequency adjustment, this leads to destructive interference and the received amplitude settles to an amplitude corresponding to the reflection properties of a ‘virtual interface’ between reference and test fluid. So the reflection coefficient R of the half-wave layer is given by: R=K
steady state amplitude leading edge amplitude
,
(4)
where K is an invariant calibration factor. Using the known properties such as the density r and the sound 1 velocity c of the reference medium as well as the sound 1 velocity of the test medium c (measured for example 3 by the ultrasound flow sensor), the density can be calculated from the reflectivity law ( Eq. (2)) and according to the notation in Fig. 3 this leads to: c 1+R , r =r 1 3 1 c 1−R 3
(5)
where no material parameter of the half-wave layer appears.
2.3. Time domain evaluation One way to describe the signal shape of the echoes occurring is to superimpose sequentially all incident and reflected waves. In the steady state for half-wave adjustment the condition of total antireflection of the layer between reference and test fluid is assumed. That is, for the same liquid as reference and test fluid there is no reflection but only transmission because of total cancellation of all waves. From various measurements it is known that this does not hold in general. Thus the following mathematical model is used to describe the principle processes. When an acoustic wave travelling in a first medium encounters the boundary of a second medium, reflected and transmitted waves are generated. It is assumed that a solid layer of uniform thickness d is placed between two different fluids and that a plane wave is normally incident on its boundary, as shown in Fig. 4. Let the acoustic impedances of the media be Z , Z and Z , respectively. Furthermore, A is the 1 2 3 0 amplitude of the incident wave and A is the amplitude 1 of the direct reflected wave. The wave with amplitude A undergoes a transmission at boundary Z /Z , a 2 1 2 reflection at Z /Z and again a transmission at Z /Z . 2 3 2 1 All the following waves A to A exhibit the same 3 n sequence but depending on their index include additional reflections at Z /Z and Z /Z . At the interface Z /Z 2 1 2 3 2 3 the reflection coefficient is negative, i.e. there is a change in phase of 180° for all waves A to A . According to 2 n the direction of incident the reflection coefficient R at ij the boundary Z /Z can be expressed as R =−R by i j ij ji using Eq. (2). It is supposed that the thickness d of the layer is equal to an integer number of the half-wave-
Fig. 3. (a) Reference measurement and (b) test measurement using resonance antireflection method.
M. Hirnschrodt et al. / Ultrasonics 38 (2000) 200–205
203
Fig. 4. Reflection and transmission at a layer.
length. This leads to:
the attenuation term, one obtains:
A =A R , 1 0 12 A =A (1−R )R (1−R ) 2 0 12 23 12 =A (1−R2 )R *a , 0 12 23 1 A =A (1−R )R R R (1−R ) 3 0 12 23 21 23 21 =A (1−R2 )R R R *a q, 0 12 23 21 23 1 e
A (1−R2 )R exp(−2a d ) 2 12 23 0 . ∑ A= 0 (8) j 1−R R exp(−2a d ) j=2 21 23 0 Compared with Eq. (6) it can be seen that total antireflection of the half-wave layer is difficult to achieve because of additional loss in energy due to attenuation.
3. Experimental verification
e A =A R R *a qn−2, n n−1 21 23 1 with a =A (1−R2 )R and q=R R . The sum of 1 0 12 23 21 23 A …A is a geometric one and for n2 results in: 2 n A (1−R2 )R 2 2 12 23 . (6) a ∑ qi= ∑ A = 0 1 j 1−R R i=0 j=2 21 23 Substituting the deduced variables for the special case Z =Z ( layer in one liquid) obtains for the finite sum: 1 3 n n ∑ a =A (1−R2 )R ∑ R2(i−1) i 0 12 21 21 i=1 i=1 R2(n−1) 21 =A (1−R2 )R . (7) 0 12 21 R2 −1 21 For n2 this sum equals A R =−A and therefore 0 21 1 total cancellation of the direct reflected wave A occurs. 1 Usually the thickness of the l/2 layer is only a few millimetres corresponding to a frequency range from 500 kHz to 2 MHz. Because of the large number of reflections inside the layer, the waves travel a long distance and so they undergo attenuation. Because the attenuation constant a of the layer varies with the 2 square of the frequency, the attenuation cannot be neglected in the frequency range used. Using the same equations as before and considering
To verify the results from the numerical simulations, a number of experiments have been carried out. With the present setup only non-flowing liquids were examined. 3.1. Experimental setup The ultrasonic transducer is driven by a sinusoidal burst of variable cycles, which is generated by an arbitrary waveform generator. The signals received by this transducer are amplified and afterwards acquired by a PCI compatible waveform digitizer board. The MatLab software environment is used for processing the data digitally. 3.2. Simulation in time domain A practically usable layer has to be a compromise between chemical resistivity and acoustic properties (attenuation, impedance). Quartzglass complies with both requirements and was chosen for the experiments. The frequency of the exciting signal was adjusted to 1 MHz, its amplitude to 10 Vpp and the number of periods was 40. The thickness of the layer was 3 mm and water was used as the reference fluid. In Fig. 5 a measured echo for water as test fluid is shown.
204
M. Hirnschrodt et al. / Ultrasonics 38 (2000) 200–205
3.3. Results and discussion
Fig. 5. Measured echo signal using water as test fluid.
To demonstrate the feasibility of the resonance antireflection method, the density of several test fluids has been calculated according to Eq. (5). Then the results have been compared with the values measured with a conventional densitometer (vibrating tube, accuracy 0.1%) acting as a reference. In Fig. 6 the relative error in density measured with the RAR method is shown. It can be seen that deviations from the reference density are smaller than ±1.5%. This is an adequate result in view of the simple plane wave evaluation algorithm which was used. In forthcoming work refined evaluation including attenuation and aperture effects will be implemented to exploit the full potential of the resonance antireflection method. As mentioned in Section 2.3 further improvements will be possible by evaluating the whole receiving signal in the time domain including transient contributions.
4. Concluding remarks
Fig. 6. Relative error in density.
Comparing this with the results of the according simulation shows minor distinctions. This indicates that deviations from the assumption of normally incident plane waves occur. Reasons for this are radiation pattern, non-uniform surface excursions and the aperture of the transducer. Furthermore in this simulation the exciting signal was generated by second-order filtering of a gated ultrasound signal, which changes the resulting signal in the transient range. Looking at the steady state region of Fig. 5 shows that the amplitude has settled at an non-zero value. Acoustic physics says that in this case there should be no reflection, but only transmission. As mentioned before, the attenuation inside the layer prevents a total antireflection of the layer. Additional errors occur as a result of changes in the sound velocity.
A new method to measure the density of liquids using ultrasonic resonance antireflection has been presented. The RAR technique is based on a measurement of the reflection coefficient at a virtual interface between a reference fluid and the test fluid. The solid layer used for separating these two liquids appears to vanish for the incident waves, if the half-wave condition is accomplished. Various numerical simulations have been performed and the results show the capability for high accuracy measurements. This has been verified by a number of measurements which fulfil the expectations from the simulations. The measurement setup automatically compensates drifts in the electronics and transducer long-term variations by means of a single transducer arrangement and extracting a reference signal from the echo signal. Forthcoming computer modelling will include reflections at the housing, the influence of different radiation pattern and the aperture of the transducer. The influence of surface contamination on the accuracy will also be considered by using data of laser Doppler vibrometer measurements.
References [1] B. Fischer, A. v. Jena, V. Magori, Ultraschall-Dichtemesser zum Messen der spezifischen Dichte eines Fluid, Eur. Patent EP 0483 491 B 1, 1995. [2] D.J. McClements, P. Fairly, Ultrasonic pulse echo reflectometer, Ultrasonics 29 (1991) 58–62. [3] J.M. Hale, Ultrasonic density measurement for process control, Ultrasonics 26 (1988) 356–357.
M. Hirnschrodt et al. / Ultrasonics 38 (2000) 200–205 [4] K.W. McGregor, Methods of ultrasonic density measurement, Australian Instrumentation and Measurement Conference (1989) 296–298. [5] J.C. Adamowski, F. Buiochi, C. Simon, E.C.N. Silva, R.A. Sigelmann, Ultrasonic measurement of density of liquids, J. Acoust. Soc. Am. 97 (1995) 354–361.
205
[6 ] A. Pu¨ttmer, R. Lucklum, B. Henning, P. Hauptmann, Improved ultrasonic density sensor with reduced diffraction influence, Sensors and Actuators A 67 (1998) 8–12. [7] J. Kushibiki, N. Akashi, T. Sannomiya, N. Chubachi, F. Dunn, VHF/UHF range bioultrasonic spectroscopy system and method, IEEE Trans. Ultras. Ferro. Freq. 42 (6) (1995) 1028–1039.
Ultrasonic characterization of liquids using resonance antireflection M. Hirnschrodt a, *, A. v. Jena b, T. Vontz b, B. Fischer b, R. Lerch a a University of Linz, Altenbergerstr. 69, A-4040 Linz, Austria b Siemens AG, ZT KM 2, Otto-Hahn-Ring 6, D-81730 Mu¨nchen, Germany
Abstract This paper presents an ultrasonic method for measuring the density of liquids with a solid layer separating a reference fluid and a test fluid. By adjusting the frequency of the exciting signal according to the thickness of the layer, it is possible to generate destructive interference of the waves reflected at the first and at the second boundary of the layer. Thus, the layer appears to vanish for the incident waves. The resulting echo signal depends only on the acoustic impedances of the reference fluid and the test fluid and the density which is of interest can be extracted. Short and long-term drifts of the electronics and the ultrasonic transducer implied are eliminated by using the well-known pulse–echo technique with additional frontwave detection. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Antireflection; Density; Liquids; Resonance; Ultrasonic
1. Introduction Density is a fundamental parameter for describing a fluid. It is an indicator of the type of fluid, its constituents and any contaminants. In conjunction with volume measurement it gives mass. In process industries, especially in the petrochemical industry, density measurement is used for process control and measurement of mass flow. There is a need for mass flow measurement meters with adequate accuracy (±1%), compact size, easy installation and low costs. These demands are met by the combination of an ultrasonic volume flow sensor with an ultrasonic density sensor. In principle an ultrasound density sensor uses the reflection at discontinuities of acoustic impedance, where the reflection coefficient is relative to the ratio of the acoustic impedance of the adjacent media [1–4]. To establish such a boundary zone, a solid buffer rod can be used, with one side directly coupled with the transducer and the other side with the fluid [5–7]. The difficulty of this approach, however, is the fact that a larger difference in the acoustic impedances between the solid and the liquid results in a lower sensitivity for changes in the density of the fluid. * Corresponding author. Fax: +49-89-636-46881. E-mail address: [email protected] (M. Hirnschrodt)
In this paper, it is shown that this limitation can be overcome by using resonance antireflection ( RAR) with a half-wave layer as a separating wall between the flow tube and the ultrasound sensor, as illustrated in Fig. 1. The frequency of the incident sound wave is adjusted so that the wavelength inside the layer is exactly twice its thickness and complete destructive interference is accomplished. The half-wave layer then acts as an ideal antireflecting coating and the reflected intensity depends only on the difference in the acoustic impedances of the two media in front of and behind the layer (‘virtual boundary’). The reference medium in the ‘pre-run’ chamber can be chosen to achieve the highest sensitivity of the measurement in the most interesting range of densities.
2. Acoustic determination of density using reference principle 2.1. Fundamentals To achieve a small influence of parameters difficult to control, such as aging of materials, transducer longterm variations and drifts in the electronics, the pulse– echo method is used for the measurement of the reflection coefficient. A single ultrasonic transducer acts in the pulse–echo mode sequentially as transmitter and
0041-624X/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S0 0 4 1 -6 2 4 X ( 9 9 ) 0 0 05 0 - 5
M. Hirnschrodt et al. / Ultrasonics 38 (2000) 200–205
201
Fig. 1. Principle of ultrasonic mass flow measurement using time-of-flight measurement for volume flow and resonance antireflection for density.
receiver for ultrasound bursts. The amplitude A of the R reflected front wave depends on the transmitted signal level A and on the acoustic impedances involved at the 0 boundary. With the reflection coefficient given by: A R= R , (1) A 0 the density can be extracted by using the well-known equations Z −Z 1 , Z=rc, R= 2 Z +Z 2 1 which results in c 1+R r =r 1 . 2 1 c 1−R 2
reflection coefficient of a water/ethanol interface. It can be seen that using steel as a reference medium, whose acoustic impedance is 30 times higher that of water, results in a change of the reflection coefficient of about 11%. Using polymethyl methacrylate (PMMA) with an approx. 2 times higher impedance leads to a sensitivity of about 105% and ethanol with a 0.65 times higher impedance results in a 125% change of reflection. With the resonance antireflection method it is possible to use transient and steady state parts of the echo signal
(2)
(3)
2.2. Resonance antireflection method Compared with the method using a solid buffer rod as reference medium the resonance antireflection method shows a higher sensitivity for changes in the density of the test liquid. This results from the better matching of the acoustic impedances by using a liquid reference medium instead of a solid. In Fig. 2 the relative change of the reflection coefficient DR/R for different referRef ence materials as a function of the acoustic impedance of various test fluids is shown, normalized for the
Fig. 2. Variation of reflection coefficient for different reference materials versus acoustic impedance.
202
M. Hirnschrodt et al. / Ultrasonics 38 (2000) 200–205
(see Fig. 5) for the reference measurement and for the interrogation of the separation layer. In Fig. 3(a) the detection of the reference signal is illustrated. Reflection takes place at all interfaces. A∞ is 0 the contribution of the reflection at the interface reference fluid/half-wave layer (Fig. 3(a)) and A is the R reflection from the interface half-wave layer/test fluid (Fig. 3(b)). Since the amplitude A∞ of the received wave 0 front is not influenced by the acoustic properties of the test fluid, it can be used to represent the incident intensity, which is necessary for the calculation of the reflection coefficient. Certainly this is only true for the small time window where the wave, reflected at the boundary Z /Z , has not yet reached the first boundary 2 3 and therefore has not yet affected the incident wave. Thus only the very first leading edge oscillations are suitable for determining the reference intensity. In the steady state condition, waves reflected at the Z /Z and 1 2 the Z /Z boundaries do interfere with each other. 2 3 Because of the sign reversal at the second interface and the precise frequency adjustment, this leads to destructive interference and the received amplitude settles to an amplitude corresponding to the reflection properties of a ‘virtual interface’ between reference and test fluid. So the reflection coefficient R of the half-wave layer is given by: R=K
steady state amplitude leading edge amplitude
,
(4)
where K is an invariant calibration factor. Using the known properties such as the density r and the sound 1 velocity c of the reference medium as well as the sound 1 velocity of the test medium c (measured for example 3 by the ultrasound flow sensor), the density can be calculated from the reflectivity law ( Eq. (2)) and according to the notation in Fig. 3 this leads to: c 1+R , r =r 1 3 1 c 1−R 3
(5)
where no material parameter of the half-wave layer appears.
2.3. Time domain evaluation One way to describe the signal shape of the echoes occurring is to superimpose sequentially all incident and reflected waves. In the steady state for half-wave adjustment the condition of total antireflection of the layer between reference and test fluid is assumed. That is, for the same liquid as reference and test fluid there is no reflection but only transmission because of total cancellation of all waves. From various measurements it is known that this does not hold in general. Thus the following mathematical model is used to describe the principle processes. When an acoustic wave travelling in a first medium encounters the boundary of a second medium, reflected and transmitted waves are generated. It is assumed that a solid layer of uniform thickness d is placed between two different fluids and that a plane wave is normally incident on its boundary, as shown in Fig. 4. Let the acoustic impedances of the media be Z , Z and Z , respectively. Furthermore, A is the 1 2 3 0 amplitude of the incident wave and A is the amplitude 1 of the direct reflected wave. The wave with amplitude A undergoes a transmission at boundary Z /Z , a 2 1 2 reflection at Z /Z and again a transmission at Z /Z . 2 3 2 1 All the following waves A to A exhibit the same 3 n sequence but depending on their index include additional reflections at Z /Z and Z /Z . At the interface Z /Z 2 1 2 3 2 3 the reflection coefficient is negative, i.e. there is a change in phase of 180° for all waves A to A . According to 2 n the direction of incident the reflection coefficient R at ij the boundary Z /Z can be expressed as R =−R by i j ij ji using Eq. (2). It is supposed that the thickness d of the layer is equal to an integer number of the half-wave-
Fig. 3. (a) Reference measurement and (b) test measurement using resonance antireflection method.
M. Hirnschrodt et al. / Ultrasonics 38 (2000) 200–205
203
Fig. 4. Reflection and transmission at a layer.
length. This leads to:
the attenuation term, one obtains:
A =A R , 1 0 12 A =A (1−R )R (1−R ) 2 0 12 23 12 =A (1−R2 )R *a , 0 12 23 1 A =A (1−R )R R R (1−R ) 3 0 12 23 21 23 21 =A (1−R2 )R R R *a q, 0 12 23 21 23 1 e
A (1−R2 )R exp(−2a d ) 2 12 23 0 . ∑ A= 0 (8) j 1−R R exp(−2a d ) j=2 21 23 0 Compared with Eq. (6) it can be seen that total antireflection of the half-wave layer is difficult to achieve because of additional loss in energy due to attenuation.
3. Experimental verification
e A =A R R *a qn−2, n n−1 21 23 1 with a =A (1−R2 )R and q=R R . The sum of 1 0 12 23 21 23 A …A is a geometric one and for n2 results in: 2 n A (1−R2 )R 2 2 12 23 . (6) a ∑ qi= ∑ A = 0 1 j 1−R R i=0 j=2 21 23 Substituting the deduced variables for the special case Z =Z ( layer in one liquid) obtains for the finite sum: 1 3 n n ∑ a =A (1−R2 )R ∑ R2(i−1) i 0 12 21 21 i=1 i=1 R2(n−1) 21 =A (1−R2 )R . (7) 0 12 21 R2 −1 21 For n2 this sum equals A R =−A and therefore 0 21 1 total cancellation of the direct reflected wave A occurs. 1 Usually the thickness of the l/2 layer is only a few millimetres corresponding to a frequency range from 500 kHz to 2 MHz. Because of the large number of reflections inside the layer, the waves travel a long distance and so they undergo attenuation. Because the attenuation constant a of the layer varies with the 2 square of the frequency, the attenuation cannot be neglected in the frequency range used. Using the same equations as before and considering
To verify the results from the numerical simulations, a number of experiments have been carried out. With the present setup only non-flowing liquids were examined. 3.1. Experimental setup The ultrasonic transducer is driven by a sinusoidal burst of variable cycles, which is generated by an arbitrary waveform generator. The signals received by this transducer are amplified and afterwards acquired by a PCI compatible waveform digitizer board. The MatLab software environment is used for processing the data digitally. 3.2. Simulation in time domain A practically usable layer has to be a compromise between chemical resistivity and acoustic properties (attenuation, impedance). Quartzglass complies with both requirements and was chosen for the experiments. The frequency of the exciting signal was adjusted to 1 MHz, its amplitude to 10 Vpp and the number of periods was 40. The thickness of the layer was 3 mm and water was used as the reference fluid. In Fig. 5 a measured echo for water as test fluid is shown.
204
M. Hirnschrodt et al. / Ultrasonics 38 (2000) 200–205
3.3. Results and discussion
Fig. 5. Measured echo signal using water as test fluid.
To demonstrate the feasibility of the resonance antireflection method, the density of several test fluids has been calculated according to Eq. (5). Then the results have been compared with the values measured with a conventional densitometer (vibrating tube, accuracy 0.1%) acting as a reference. In Fig. 6 the relative error in density measured with the RAR method is shown. It can be seen that deviations from the reference density are smaller than ±1.5%. This is an adequate result in view of the simple plane wave evaluation algorithm which was used. In forthcoming work refined evaluation including attenuation and aperture effects will be implemented to exploit the full potential of the resonance antireflection method. As mentioned in Section 2.3 further improvements will be possible by evaluating the whole receiving signal in the time domain including transient contributions.
4. Concluding remarks
Fig. 6. Relative error in density.
Comparing this with the results of the according simulation shows minor distinctions. This indicates that deviations from the assumption of normally incident plane waves occur. Reasons for this are radiation pattern, non-uniform surface excursions and the aperture of the transducer. Furthermore in this simulation the exciting signal was generated by second-order filtering of a gated ultrasound signal, which changes the resulting signal in the transient range. Looking at the steady state region of Fig. 5 shows that the amplitude has settled at an non-zero value. Acoustic physics says that in this case there should be no reflection, but only transmission. As mentioned before, the attenuation inside the layer prevents a total antireflection of the layer. Additional errors occur as a result of changes in the sound velocity.
A new method to measure the density of liquids using ultrasonic resonance antireflection has been presented. The RAR technique is based on a measurement of the reflection coefficient at a virtual interface between a reference fluid and the test fluid. The solid layer used for separating these two liquids appears to vanish for the incident waves, if the half-wave condition is accomplished. Various numerical simulations have been performed and the results show the capability for high accuracy measurements. This has been verified by a number of measurements which fulfil the expectations from the simulations. The measurement setup automatically compensates drifts in the electronics and transducer long-term variations by means of a single transducer arrangement and extracting a reference signal from the echo signal. Forthcoming computer modelling will include reflections at the housing, the influence of different radiation pattern and the aperture of the transducer. The influence of surface contamination on the accuracy will also be considered by using data of laser Doppler vibrometer measurements.
References [1] B. Fischer, A. v. Jena, V. Magori, Ultraschall-Dichtemesser zum Messen der spezifischen Dichte eines Fluid, Eur. Patent EP 0483 491 B 1, 1995. [2] D.J. McClements, P. Fairly, Ultrasonic pulse echo reflectometer, Ultrasonics 29 (1991) 58–62. [3] J.M. Hale, Ultrasonic density measurement for process control, Ultrasonics 26 (1988) 356–357.
M. Hirnschrodt et al. / Ultrasonics 38 (2000) 200–205 [4] K.W. McGregor, Methods of ultrasonic density measurement, Australian Instrumentation and Measurement Conference (1989) 296–298. [5] J.C. Adamowski, F. Buiochi, C. Simon, E.C.N. Silva, R.A. Sigelmann, Ultrasonic measurement of density of liquids, J. Acoust. Soc. Am. 97 (1995) 354–361.
205
[6 ] A. Pu¨ttmer, R. Lucklum, B. Henning, P. Hauptmann, Improved ultrasonic density sensor with reduced diffraction influence, Sensors and Actuators A 67 (1998) 8–12. [7] J. Kushibiki, N. Akashi, T. Sannomiya, N. Chubachi, F. Dunn, VHF/UHF range bioultrasonic spectroscopy system and method, IEEE Trans. Ultras. Ferro. Freq. 42 (6) (1995) 1028–1039.