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Acoustic field generated by an innovative airborne power ultrasonic system with reflectors for coherent radiation
Ultrasonics 99 (2019) 105963
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Acoustic field generated by an innovative airborne power ultrasonic system with reflectors for coherent radiation
T
R.R. Andrésa,b,⁎, A. Pintoa, I. Martíneza, E. Rieraa a b
Departamento de Sensores y Sistemas Ultrasónicos (DSSU), ITEFI, CSIC, Serrano 144, 28006 Madrid, Spain Escuela Técnica Superior de Ingenieros Industriales (ETSII), Universidad Politécnica de Madrid (UPM), Calle de José Gutiérrez Abascal 2, 28006 Madrid, Spain
ARTICLE INFO
ABSTRACT
Keywords: High-power ultrasound Ultrasonic transducers Acoustic pressure distribution Directivity patterns Finite element analysis
In order to obtain the maximum efficiency in industrial processes assisted by airborne power ultrasound, the ultrasonic systems must be capable of generating an acoustic field with a maximum energy concentration in the desired areas. In this paper, the acoustic performance of two different ultrasonic systems is presented. The first system corresponds to an airborne power ultrasonic transducer with a flat rectangular plate radiator, and the second system is composed by the same transducer mounted in a set of reflectors that allow the generation of coherent radiation. The acoustic pressure field for each system has been determined numerically and the spatial pattern has been experimentally measured. In the experiment, the system with reflectors obtained higher pressure amplitude in a wider area, due to the coherent radiation achieved. The directivity pattern obtained in the experiment confirms this coherent radiation field. This is the first time that the acoustical behavior of two different ultrasonic systems with flat rectangular radiator, vibrating in a complex flexural mode, has been numerically and experimentally described and compared in terms of pressure amplitude distribution and directivity pattern.
1. Introduction The use of power ultrasound has become an innovative, efficient and green technology for use in some industrial applications. Among these applications, the efficiency of defoaming [1], particle agglomeration [2] and food dehydration [3] are enhanced with the use of airborne power ultrasounds. This sustainable technology needs an airborne power ultrasonic transducer (APUT) to work in a required operational mode at a high power regime in order to generate the desired ultrasonic field in the action area. The ultrasonic energy, generated by the APUT, is capable of activating some mechanisms that produce permanent changes in the treated medium. The APUT is composed of a piezoelectric Langevin-type sandwich [4], a mechanical amplifier or horn, and an extensive radiator, that provides the required impedance to match with the media [5]. Different shapes of the radiator have been designed for industrial purposes: circular [6], rectangular [7] and cylindrical [8]. The profile of the extensive radiator may be modified in order to generate ultrasonic fields with different characteristics [5]. In the case of circular and rectangular radiators, a stepped profile enables a coherent field in free field, similar, but not equal, to the acoustic field ⁎
generated by a piston [9], whereas a grooved profile, in the case of circular radiators, allows a focused field. At the same time, it is important to take into account the fact that the plate radiator generates acoustic energy from the vibration of its two faces. In order to use all this energy, an ultrasonic system with reflectors (SWR) was developed by [10] for an APUT with an operational frequency of 9.7 kHz in the sonic range. This work considers the basis of the acoustic system introduced in [10], resized for an APUT with flat rectangular radiator working in an operational mode with 12 nodal lines (12NL) at 21 kHz [11]. This innovative configuration increases the efficiency of the system by using the energy generated in both faces of the plate and a more versatile performance by building reflectors to obtain a coherent field, instead of the steps of the radiating plate. It is important to mention that the behavior of a piston implies that the whole radiating surface vibrates with the same amplitude and phase, generating a plane wave. The acoustic field generated in this situation has been widely studied and can be divided into a near field and a far field [12]. The ultrasonic system presented in this publication seeks the generation of a coherent field similar to the field generated by a piston, but not identical. This means that the consideration of near field and far field are mere references in this manuscript.
Corresponding author. E-mail address: [email protected] (R.R. Andrés).
https://doi.org/10.1016/j.ultras.2019.105963 Received 10 May 2018; Received in revised form 6 July 2019; Accepted 13 July 2019 Available online 15 July 2019 0041-624X/ © 2019 Elsevier B.V. All rights reserved.
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mode with twelve nodal lines (12|0) at a frequency near 21 kHz. The transducer has been improved with a system of reflectors to enable coherent radiation patterns with high-intensity levels and an electroacoustic efficiency of around 70%. Usually, the generation of coherent radiation was achieved by designing a stepped geometry to the radiating profile of the plate [5]. Steps, with a height size of a half-wavelength in the propagation medium, were required at the nodal lines of the plate. Media with small wavelengths, such as air, allow an affordable step performance, but step sizes required for media with much larger wavelengths, such as water, makes it impractical to design a stepped radiator. To address this, a reflector structure was added to the flat rectangular plate transducer. These reflectors were placed at a 45 degrees angle with respect to the two parallel vibrating surfaces of the rectangular plate to duplicate the radiating surface of the transducer. Thus, the acoustic energy emitted from both sides of the radiator was taken advantage of to obtain the desired effects of a coherent acoustic field, also increasing the electroacoustic efficiency of the system. The reflector structure is composed of a system of channels capable of putting in phase the radiation of different zones of the flat rectangular plate that vibrate in counter-phase. The effect of this structure is shown in Fig. 2. The ultrasonic field generated by the internodal sectors of the plate, vibrating in a flexural mode, propagates in counter-phase to the reflectors, as can be observed in Fig. 2a. The channels structure is capable of putting in phase the ultrasonic waves after the first reflection, and subsequently transmitting a coherent field in free field: As mentioned before, the mechanical amplifier has been lengthened λ/2 in the narrow section because the protective housing of the transducer may interfere with the ultrasonic waves generated by the flat rectangular plate in their path to the reflectors. With this extension, the protective housing remains outside the reflectors system and the interferences are minimized. This can be observed in Fig. 2b, where the narrow section of the horn is 3λ/4 long. The appearance of the whole system is shown in Fig. 3:
Fig. 1. Airborne power ultrasonic transducer with a rectangular plate radiator.
In the following sections, the radiated fields, in the near field, generated by this new APUT system will be presented and analyzed numerically and experimentally, focusing on the pressure amplitude distribution at different distances and on the directivity patterns obtained in the far field, in comparison with the APUT with flat rectangular plate without the reflectors system. Even if the idea of attaching a reflectors system to an APUT with flat rectangular radiator for a coherent acoustic radiation was presented previously [10], this is the first time that the acoustic behavior of such system has been numerically and experimentally analyzed with the radiator vibrating in a complex flexural mode, thus validating a numerical model for this system. The results obtained after this analysis confirm that the system of reflectors allows coherent radiation, compared to the APUT with flat rectangular transducer without reflectors. 2. Description of the ultrasonic system The APUT described in [11] basically consists of a piezoelectric Langevin-type sandwich including four stacked piezoceramic rings, prestressed at 25 MPa, a half-wavelength mechanical amplifier (horn); and an extensive flat radiator with rectangular geometry that allows a good impedance match with the gas medium and a high-intensity ultrasonic field. Fig. 1 shows the airborne power ultrasonic transducer. The desired operational mode of the transducer corresponds to an extensional mode of the ultrasonic vibrator (Langevin-type sandwich and horn) which drives the radiator into resonance in one of its flexural modes. In the present study the plate radiator vibrates in a flexural
3. Acoustic field generated by this new system 3.1. Numerical simulation of the ultrasonic field The determination of the acoustic field generated by this ultrasonic system can be carried out using numerical and experimental methods. The numerical determination of the ultrasonic field has been calculated using FEM methods with the simulation software COMSOL Multiphysics®. The numerical analysis of the ultrasonic transducer with
Fig. 2. Food dehydration system with an APUT and a reflector system. 2
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Fig. 3. Two views of the ultrasonic system with reflectors.
a rectangular flat plate radiator has already been presented in [11], where the operational mode with twelve nodal lines (12|0) has been found at 21,049 Hz. The ultrasonic field generated by this transducer can be obtained with a multiphysics simulation in which the structural mechanics module simulates the vibration of the rectangular radiator, and the acoustics module simulates the ultrasonic field. The displacements that take place in the surface of the radiator excite the particles of the fluid creating an acoustic wave that propagates along the fluid domain. The processing capacity of the computer is critical when carrying on FEM simulations, especially in the case of 3D simulations. The basis of the finite element method is that, when it is necessary to solve an equation in a certain domain, this domain can be divided into small elements in which the equation can be easily solved, and the solution for each element can be used as a boundary condition for the next one. This process requires that the size of each element to be as small as possible in order to insure a good convergence of the solution. Therefore, the smaller the size of each element, the larger the number of elements, and the higher the required processing capacity of the computer. Shannon’s sampling theorem leads to the idea of using a fixed amount of elements per wavelength. In [13], an analysis of the error obtained for a different type of elements and the number of elements per wavelength is presented. In the case of quadratic elements, and for a long duct filled with air, the conclusion obtained in [13] was that two elements per wavelength correspond to an error of about 10 percent. Therefore, it is recommendable to have at least two quadratic elements per wavelength. In this case, the transducer is vibrating at 21,049 Hz in air, meaning that the ultrasonic waves have a wavelength around 16 mm (considering that the sound speed in air is 343 m/s). According to this, the maximum size of the elements should be 8 mm, even though smaller elements are used. The fluid where the acoustic propagation is simulated is air at 20 °C, considered a linear elastic fluid, in which thermoviscous losses are considered negligible. The equation solved in the FEM model corresponds to the linear wave equation (Eq. (1)) in a lossless medium [14]:
·
1
p
2p =0 c2
simulation may be quite large, depending on the size of the domain and the frequency of the wave. In this case, 2D and 3D simulations have been carried out for the ultrasonic field generated by the flat rectangular plate transducer, which is excited with a monochromatic continuous wave at around 21 kHz, in order to induce the desired flexural mode with twelve nodal lines. The transducer can be observed in Fig. 1. A schematic representation of the transducer is depicted in Fig. 4a, with the operational mode (12|0) presented in Fig. 4b: In the case of a rectangular piston, the identification of the near field and the far field could be done theoretically using the Rayleigh distance which, for plane radiators acting as a piston, can be determined using Eq. (2) [15]:
D=
2 fa2 2c
(2)
In Eq. (2), a is half of the largest dimension of the radiator, f is the propagation frequency and c represents the sound speed in the medium. The separation between the near field and the far field is located at a distance of 1/π of the Rayleigh distance. This theoretical equation is suitable for a rectangular piston. According to Eq. (2), the Rayleigh distance of a rectangular piston with these dimensions is 15.7 m, meaning that the separation between the near and far field is located at approximately 5 m from the source. However, the transducer is not acting as a piston because it vibrates in a flexural mode, and the previous calculation should be considered as a mere reference. In order to set an approximate frontier between a hypothetic near field and far field, a 2D numerical determination has been done, obtaining the ultrasonic field in the plane XY, with a maximum element size of /6, to delimit the size of the 3D simulation to an area near the transducer, with a pressure distribution similar to the one of an ideal piston. The simulations are done considering free field propagation, by defining Perfectly Matched Layers (PML’s) in the boundaries of the fluid domains. The 2D simulation allows a larger distance with a higher resolution because the number of elements, thus the required computational resources, is much smaller than in a 3D simulation. The result of this analysis can be observed in Fig. 5. The acoustic field is generated by the transducer vibrating at its operational mode with 12NL at a frequency of 20,481 Hz. A simulated continuous wave excitation of 200 W is shown in Fig. 5a and the acoustic pressure evolution along the x-axis is shown in Fig. 5b: As can be observed in Fig. 5b, the pressure amplitude distribution along the axis approximately follows the pressure distribution of the acoustic field generated by a piston [12], with an alternation of maxima and minima of pressure amplitude near the radiator, and a progressive amplitude decrease further away. The pressure distribution of the rectangular plate transducer, under the defined operational conditions,
(1)
where p is the acoustic pressure, and c are the density and sound speed of the fluid and represents the angular frequency of the wave. 3.1.1. Numerical simulation of the acoustic field generated by a flat rectangular plate transducer vibrating in a flexural mode As mentioned before, the computational resources required in a 3D 3
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Fig. 4. (a) Schematic representation of the transducer. (b) Operational mode with 12 nodal lines around 21 kHz.
shows an alternation of maxima of pressure up to one meter from the transducer, and an amplitude decrease after that distance, but this decrease is not really progressive because other areas with maxima appear. The limit between an area considered as near field and the far field can be set, in this situation, at about one meter from the radiator. The 3D simulation comprises a length of 1.2 m in order to cover the area of interest. This 3D simulation allows the possibility of obtaining 2D slices parallel to the surface of the radiator, in order to view the acoustic evolution in the near field (Fig. 6): Fig. 6 shows pressure nodes affected by the nodal lines of the radiator, and how the pressure map becomes more homogeneous when
the distance from the radiator is increased. Two areas with maximum pressure values appear in Fig. 6f, corresponding to the YZ slice at a distance of 968 mm from the transducer. The energy focuses on these areas, resulting in two directional lobes. These lobes can be observed in Fig. 7 and in the directional patterns presented in section 4, and also in Fig. 21b: 3.1.2. Numerical simulation of the acoustic field generated by the ultrasonic system with reflectors The numerical simulation of the acoustic field generated by the ultrasonic system with reflectors has been carried out in a 3D model.
Fig. 5. 2D numerical simulation of the acoustic field generated by a flat rectangular APUT vibrating at its operational mode at 20,481 Hz. (a) Ultrasonic field in the XY plane. (b) 1D continuous wave axial pressure variations. 4
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Fig. 6. Slices in the YZ plane, parallel to the flat radiator, at different distances.
Fig. 7. Acoustic pressure (Pa) amplitude distribution in the plane XZ.
computational resources, a two-step simulation has been done, obtaining the amplitude pressure map at the output of the SWR in the first step, and using this result as an input in the second step, the free field simulation. The axis orientation in this simulation is shown in Fig. 8: As mentioned before, the first simulation tries to determine the nature of the ultrasonic field generated by a virtual radiator that would be the output of the ultrasonic system, which corresponds to the YZ plane in Fig. 8. The operational mode of the rectangular plate transducer has a shape with 12 nodal lines (12|0), at a frequency of 20,481 Hz. In order to reduce the computational resources required to do this simulation, and taking into account that the model is symmetric, only a quarter of the system has been analyzed, applying symmetric boundary conditions and rebuilding the whole model for presentation purposes. The first step consists of the determination of the ultrasonic field at the output of the SWR, which is the amplitude pressure field of the virtual radiator. The acoustic field inside the reflectors system and at the output is presented in Fig. 9: The pressure amplitude distribution presented in Fig. 9b is introduced as an initial value for the free field simulation, in order to determine the acoustic field generated by the whole system. This acoustic field, determined numerically under free field conditions, is presented in Fig. 10, where the XY plane and the XZ plane are shown:
Fig. 8. Schematic representation of the system with reflectors.
The computational resources required in this simulation are higher because it is necessary to simulate two acoustic fields, the field obtained in the space between the transducer and the reflectors, and the field that the system generates into the free field. In order to reduce these 5
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Fig. 9. (a) Ultrasonic field inside the reflectors system. (b) Acoustic pressure in the virtual radiator.
On the other side, YZ planes, parallel to the virtual radiator are also presented in Fig. 11 to view the acoustic evolution near the radiator: Comparing the pressure distribution obtained with the flat rectangular plate (Figs. 5–7) and the pressure distribution obtained with the
ultrasonic system (Figs. 10 and 11), it can be seen that the latter doubles the area of interest, and that there are higher pressure amplitudes in the free field. This event is produced by constructive interferences that occur after putting in phase the acoustic waves with the reflectors.
Fig. 10. Acoustic pressure (Pa) distribution under free field conditions, generated by the ultrasonic system with reflectors.
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Fig. 11. Slices in the YZ plane, parallel to the radiation surface of the system with reflectors, at different distances.
The experimental analysis will confirm the improvements obtained with the SWR and will validate the numerical model used in these simulations.
continuously along the axis in order to first identify the limit between the near and far field, and then determine the location of maximum pressure amplitude points in the near field. The acoustic pressure amplitudes were determined from the voltage measurements, taken with a spatial resolution of 1 mm associated with the limitations of the measuring setup. Then, 2D raster scans were carried out in planes parallel to the radiating surface of the transducer where the maxima in the near field are located. In these scans, sweeps cover the desired plane, with continuous displacements along the y-axis, and steps of 1 mm in the z-axis. Pressure measurements in planes perpendicular to the transducer emitter surface have been obtained with 2D Raster scans with a continuous movement along the y axis and 1 mm steps in the x axis. The experimental setup is composed by an ultrasonic controller, whose task is to drive the transducer into the desired operational mode and track this mode even if the working frequency varies. The signal goes to an impedance matching unit through the amplifier and then to the transducer, which vibrates at the required frequency and generates the ultrasonic field that is measured as explained before. The electrical output of the microphone registered at each point is stored on a PC. The output voltage level from the microphone is then converted to the equivalent acoustic pressure (Pa), using the sensitivity of the microphone (1 mV/Pa). The block diagram of the measurement setup is shown in Fig. 12: As mentioned before, the experimental determination of the ultrasonic pressure amplitude field has been done in a semi-anechoic chamber, with dimensions 5 × 3,3 × 3,5 m3 (57,75 m3). The semi-anechoic chamber has a reflecting floor and absorbing enclosures, as can be observed in Fig. 13:
3.2. Experimental setup for the ultrasonic field determination The ultrasonic field generated under operational conditions is intended to have a sound pressure level higher than 150 dB at the operational frequency around 21 kHz. An electric supply between 150 W and 200 W is necessary to produce such a high pressure level, and should be the operational power supply. Nevertheless, this sound pressure level is very high even for the measurement transducer (microphone GRAS 40DP), which is not capable of withstanding such extreme amplitudes. This comes about because this type of condenser microphones have a membrane that reacts to the incident acoustic pressure by moving back and forth, and as a result, the capacitance of the condenser analogously to the frequency and amplitude of the sound wave changes. If the acoustic pressure amplitude is as high as 150 dB, this thin membrane may break and result in the failure of the microphone. For this reason, a linear approximation has been done in the experimental determination of the acoustic field generated by the rectangular plate transducer and by the SWR. The excitation level in all cases has been 20 W. The experimental characterization of the acoustic pressure amplitude field generated by the APUT with flat rectangular plate both with and without a reflector system has been carried out in a hemi-anechoic chamber, where a PC-controlled 3D measuring system was used. The X, Y, Z coordinates related to the microphone position are governed by means of numerical control equipment (Labview® code), and they are sent to an analog treatment stage. 2D raster scans, which measure the SPL, have been done with a 1/8″ pressure microphone (GRAS 40DP), capable of measuring low frequency ultrasound. The measuring process consists of an initial 1D scan along the axis normal to the surface of the transducer with the microphone moving
3.2.1. Ultrasonic field generated by the flat rectangular plate transducer without reflectors This first determination is the ultrasonic field generated by the transducer without the reflectors system, shown in Fig. 1, and with the axis orientation represented in Fig. 4. Firstly, a 1D linear scan along xaxis allows the location of the maximum and minimum values that 7
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Fig. 12. Block diagram for the ultrasonic field experimental setup.
appear in the near field. In Fig. 14, all these distances are identified. The x-axis represents the separation to the plate, and the y-axis represents the microphone response in volts, analogous to the sound pressure amplitude obtained at each point: The limit between the near and far field appears at 1129 mm from the radiator. In the near field, there are six distances that correspond to maximum values of pressure amplitude (38 mm, 131 mm, 300 mm, 478 mm and 601 mm). As mentioned before, the measurements have
been done for an excitation of 20 W. The slices, in plane YZ, parallel to the surface of the plate, at each distance, are shown in Fig. 15: The nodal lines can be easily observed, as the measurements are taken in the near field, although they are losing resolution because of the spherical propagation of the waves. The last figure corresponds to the limit between the near and far field, with a more homogeneous field in the slice. The ultrasonic field in the planes XY and XZ (Fig. 16) are also
Fig. 13. Semi-anechoic chamber where the experimental ultrasonic field determination has been done.
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Fig. 14. Ultrasonic field along the axis of the radiator of the transducer without reflectors.
Fig. 15. 2D ultrasonic field in the plane YZ at different distances from the radiator without reflectors.
described. The maxima and minima are perfectly identified in the near field, and also the uniformity in the far field, but with much lower amplitude due to the air absorption at 21 kHz and spherical propagation of ultrasonic waves: As can be observed in Figs. 5–7; and in Figs. 15 and 16, the numerical simulation and the experimental determination show a good correlation, validating the model used in this case.
orientation is shown in Fig. 8, and the identification of the near and far field is represented in Fig. 17: The limit between the near and far field appears at 2612 mm from the radiator. In the near field, there are four distances that correspond to maximum values of pressure amplitude (0 mm, 248 mm, 419 mm, 549 mm, and 1083 mm). The slices, in plane YZ, parallel to the surface of the plate, at each distance, are shown in Fig. 18: The ultrasonic field is more uniform after putting the ultrasonic waves in phase. The central line that appears for X = 0 corresponds to a surface of the radiator. The field becomes more homogeneous when moving away from the surface. The field in the planes XY and XZ has been also determined (Fig. 19). The results obtained after the experimental determination reflect
3.2.2. Ultrasonic field generated by the ultrasonic system with reflectors Using the same methodology applied in the previous section, the ultrasonic pressure amplitude field generated by the SWR has been described. In this case, the radiating surface considered has been the coherent field coming out of the structure once the ultrasonic waves have reflected in the structure and have been put in phase. The axis 9
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Fig. 16. 2D ultrasonic field in the perpendicular planes to the transducer’s radiation surface. (a) Plane XY. (b) Plane XZ.
the improvements obtained when using the reflectors, confirming the expectations which resulted from in the numerical analysis.
order to improve the versatility of the transducer and to double the efficiency of the system (using both faces of the radiator), this system with reflectors was developed. The directivity measurements have been done in an anechoic room located in the facilities of the Instituto de Tecnologías Físicas y de la Información “Leonardo Torres Quevedo”, CSIC, in Madrid (Spain). This chamber has operational dimensions of 7.5 × 5.5 × 5.5 m3. The cut-off frequency is 80 Hz, so the chamber behaves as a free field above that frequency. All the enclosures of the chamber are covered with wedges made of mineral wool, in order to maximize the absorbing surface inside the chamber. The acoustic
4. Directivity of this new system The main objective of the ultrasonic SWR is to generate coherent ultrasonic radiation in free field. Usually, the application of steps in the surface of the radiator is essential in the generation of a coherent field [5], nevertheless, only the energy generated by the radiating surface is used, neglecting the energy radiated by the rear face of the plate; and, as mentioned before, plates with steps built in are not very versatile. In
Fig. 17. Ultrasonic field in the axis normal to the radiating surface of the system with reflectors. 10
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Fig. 18. 2D ultrasonic field in the plane YZ at different distances from the radiating surface of the system with reflectors.
Fig. 19. 2D ultrasonic field in the perpendicular planes to the radiation surface of the ultrasonic system with reflectors. (a) Plane XY. (b) Plane XZ.
properties of the chamber satisfy the requirements indicated in the Annex A of the Spanish standard UNE-EN-ISO 3745:2012: “Acoustics - Determination of sound power levels and sound energy levels of noise sources using sound pressure - Precision methods for anechoic rooms and hemi-anechoic rooms”, with the general procedure for the qualification of anechoic and hemi-anechoic rooms. The anechoic chamber can be observed in Fig. 20: The measurements were done with a 1/8″ pressure microphone (GRAS 40DP) placed at a distance of 7.8 m, in the far field. The
measurement setup is similar to the one described in the ultrasonic field characterization (Fig. 12), for a low power excitation (20 W). The emitter in each case was bolted to a rotating structure capable of pivoting in steps of one degree in order to measure the acoustic pressure generated by the emitter in a sector of 180°. The directivity of each system has been determined for the planes XY and XZ, following the directional specifications shown in Figs. 4 and 8, respectively. The results obtained after the measurement campaign are shown in Fig. 21. 11
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Fig. 20. Anechoic chamber for the directivity determination of the system without and with reflectors.
Fig. 21. Directivity of the two ultrasonic systems. (a) Flat rectangular plate, plane XY, horizontal direction. (b) Flat rectangular plate, plane XZ, vertical direction. (c) Ultrasonic system with reflectors, plane XY, horizontal direction. (d) Ultrasonic system with reflectors, plane XZ, vertical direction. 12
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The ultrasonic SWR shows a very directional behavior (Fig. 21c and d), similar to a piston, while the directivity of the transducer without SWR presents two main lobes with angles around 10° and −10° with the normal direction in the horizontal plane (XY plane).
dehydrated, environmental conditions (temperature, humidity), or the use of airflow in the process.
5. Conclusions
This work has been supported by the project DPI2012-37466-C0301 funded by the Spanish Ministry of Economy and Competitiveness. We would like to thank Mr. Ángel Guinot for his kind assistance during the measurement campaigns in the acoustic chambers, for the determination of the acoustic field and directivity pattern of the two systems analyzed.
Acknowledgments
An APUT with rectangular radiator for airborne applications has been numerically designed, developed and experimentally validated at low power conditions. The active part of this system, the transducer, has a very high quality factor (Q ≈ 13,000), a narrow bandwidth (1.59 Hz), an electroacoustic efficiency of about 80% and a resonance frequency around 21,100 Hz. A system with reflectors has been attached to the airborne power ultrasonic transducer as a new system to increase the global efficiency of the system and to generate coherent ultrasonic radiation in free field, putting in phase the ultrasonic waves generated by the transducer. The acoustic behavior of the whole system has been analyzed by numerical and experimental means. The numerical analysis has been done using the FEM software COMSOL Multiphysics®. The simulation shows an acoustic field with higher pressure amplitude in a wider area of interest when using the reflectors system. The experimental determinations have validated the numerical models and have confirmed the expected behavior of both configurations. These determinations have been done with two different experiments for the APUT without and with reflectors: a measure of the ultrasonic field in a semi-anechoic chamber and the directivity determination in an anechoic room. Our experimental results demonstrate for the first time the ability to use reflecting structures coupled to high power transducers to generate intense and coherent acoustic fields. The planar sheet-steps of these structures are mechanically attached to the planar displacement nodes of the vibrating surface of the plate, producing a coherent field. Our whole ultrasonic system, including the reflectors, shows a high directivity, concentrating the acoustic energy in the axial direction, while the system without reflectors radiates the acoustic energy forming 10° angles with the axis. This new system provides versatility for the actuation of plate-based transducers as these structures can be modified or replaced by others depending on the mode of vibration selected for each specific desired application. Future research lines will test the performance of this ultrasonic system in real food dehydration experiments under different operational conditions such as the nature of the food samples to be
References [1] G. Rodríguez, E. Riera, J.A. Gallego-Juárez, V.M. Acosta, A. Pinto, I. Martínez, et al., Experimental study of defoaming by air-borne power ultrasonic technology, Phys. Proc. 3 (2010) 135–139. [2] E. Riera, I. González-Gómez, G. Rodríguez, J.A. Gallego-Juárez, Ultrasonic agglomeration and preconditioning of aerosol particles for environmental and other applications, in: J.A. Gallego-Juárez, K.F. Graff (Eds.), Power Ultrasonics, Woodhead Publishing, Oxford, 2015, pp. 1023–1058. [3] S. de la Fuente-Blanco, E. Riera-Franco de Sarabia, V.M. Acosta-Aparicio, A. BlancoBlanco, J.A. Gallego-Juárez, Food drying process by power ultrasound, Ultrasonics 44 (Supplement 1) (2006) e523–e527. [4] E.A. Neppiras, The pre-stressed piezoelectric sandwich transducer, Ultrason. Int. 1973 (1973) 295–302. [5] J.A. Gallego-Juárez, G. Rodriguez, V.M. Acosta, E. Riera, Power ultrasonic transducers with extensive radiators for industrial processing, Ultrason. Sonochem. 17 (2010) 953–964. [6] E. Riera, J.A. Gallego-Juárez, G. Rodríguez, V.M. Acosta, E. Andrés, Application of high-power ultrasound for drying vegetables, in: Forum Acusticum, Sevilla, 2002. [7] S. de la Fuente, E. Riera, V.M. Acosta, A. Blanco, J.A. Gallego-Juárez, Food drying process by power ultrasound, Ultrasonics 44 (Supplement 1) (2006) e523–e527. [8] J.V. García-Pérez, J.A. Carcel, A. Mulet, E. Riera, J.A. Gallego-Juarez, Ultrasonic drying for food preservation, Power Ultrasonics, Woodhead Publishing, Oxford, 2015, pp. 875–910. [9] L. Elvira, E. Riera, J.A. Gallego-Juárez, Study of the near field radiated by stepped plate ultrasonic transducers in air, Ultrasonics International 93, ButterworthHeinemann, 1993, pp. 181–184. [10] J.A. Gallego-Juárez, G. Rodríguez, E. Riera, F. Vázquez, C. Campos-Pozuelo, V.M. Acosta, Recent developments in vibrating-plate macrosonic transducers, Ultrasonics 40 (2002) 889–893. [11] R.R. Andrés, V.M. Acosta, M. Lucas, E. Riera, Modal analysis and nonlinear characterization of an airborne power ultrasonic transducer with rectangular plate radiator, Ultrasonics 82 (2018) 345–356. [12] L.E. Kinsler, A.P. Frey, Fundamentals of Acoustics, John Wiley & Sons, 1950. [13] S. Marburg, Discretization requirements: how many elements per wavelength are necessary? in: S. Marburg, B. Nolte (Eds.), Computational Acoustics of Noise Propagation in Fluids - Finite and Boundary Element Methods, Springer Berlin Heidelberg, Berlin, Heidelberg, 2008, pp. 309–332. [14] Acoustics Module User's Guide, version 4.3b, COMSOL Inc. [15] H.L. Kuntz, E.L. Hixson, W.W. Ryan, The Rayleigh distance and geometric nearfield size of nonplane sound radiators, J. Acoust. Soc. Am. 74 (1983) S82–S83.
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Acoustic field generated by an innovative airborne power ultrasonic system with reflectors for coherent radiation
T
R.R. Andrésa,b,⁎, A. Pintoa, I. Martíneza, E. Rieraa a b
Departamento de Sensores y Sistemas Ultrasónicos (DSSU), ITEFI, CSIC, Serrano 144, 28006 Madrid, Spain Escuela Técnica Superior de Ingenieros Industriales (ETSII), Universidad Politécnica de Madrid (UPM), Calle de José Gutiérrez Abascal 2, 28006 Madrid, Spain
ARTICLE INFO
ABSTRACT
Keywords: High-power ultrasound Ultrasonic transducers Acoustic pressure distribution Directivity patterns Finite element analysis
In order to obtain the maximum efficiency in industrial processes assisted by airborne power ultrasound, the ultrasonic systems must be capable of generating an acoustic field with a maximum energy concentration in the desired areas. In this paper, the acoustic performance of two different ultrasonic systems is presented. The first system corresponds to an airborne power ultrasonic transducer with a flat rectangular plate radiator, and the second system is composed by the same transducer mounted in a set of reflectors that allow the generation of coherent radiation. The acoustic pressure field for each system has been determined numerically and the spatial pattern has been experimentally measured. In the experiment, the system with reflectors obtained higher pressure amplitude in a wider area, due to the coherent radiation achieved. The directivity pattern obtained in the experiment confirms this coherent radiation field. This is the first time that the acoustical behavior of two different ultrasonic systems with flat rectangular radiator, vibrating in a complex flexural mode, has been numerically and experimentally described and compared in terms of pressure amplitude distribution and directivity pattern.
1. Introduction The use of power ultrasound has become an innovative, efficient and green technology for use in some industrial applications. Among these applications, the efficiency of defoaming [1], particle agglomeration [2] and food dehydration [3] are enhanced with the use of airborne power ultrasounds. This sustainable technology needs an airborne power ultrasonic transducer (APUT) to work in a required operational mode at a high power regime in order to generate the desired ultrasonic field in the action area. The ultrasonic energy, generated by the APUT, is capable of activating some mechanisms that produce permanent changes in the treated medium. The APUT is composed of a piezoelectric Langevin-type sandwich [4], a mechanical amplifier or horn, and an extensive radiator, that provides the required impedance to match with the media [5]. Different shapes of the radiator have been designed for industrial purposes: circular [6], rectangular [7] and cylindrical [8]. The profile of the extensive radiator may be modified in order to generate ultrasonic fields with different characteristics [5]. In the case of circular and rectangular radiators, a stepped profile enables a coherent field in free field, similar, but not equal, to the acoustic field ⁎
generated by a piston [9], whereas a grooved profile, in the case of circular radiators, allows a focused field. At the same time, it is important to take into account the fact that the plate radiator generates acoustic energy from the vibration of its two faces. In order to use all this energy, an ultrasonic system with reflectors (SWR) was developed by [10] for an APUT with an operational frequency of 9.7 kHz in the sonic range. This work considers the basis of the acoustic system introduced in [10], resized for an APUT with flat rectangular radiator working in an operational mode with 12 nodal lines (12NL) at 21 kHz [11]. This innovative configuration increases the efficiency of the system by using the energy generated in both faces of the plate and a more versatile performance by building reflectors to obtain a coherent field, instead of the steps of the radiating plate. It is important to mention that the behavior of a piston implies that the whole radiating surface vibrates with the same amplitude and phase, generating a plane wave. The acoustic field generated in this situation has been widely studied and can be divided into a near field and a far field [12]. The ultrasonic system presented in this publication seeks the generation of a coherent field similar to the field generated by a piston, but not identical. This means that the consideration of near field and far field are mere references in this manuscript.
Corresponding author. E-mail address: [email protected] (R.R. Andrés).
https://doi.org/10.1016/j.ultras.2019.105963 Received 10 May 2018; Received in revised form 6 July 2019; Accepted 13 July 2019 Available online 15 July 2019 0041-624X/ © 2019 Elsevier B.V. All rights reserved.
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mode with twelve nodal lines (12|0) at a frequency near 21 kHz. The transducer has been improved with a system of reflectors to enable coherent radiation patterns with high-intensity levels and an electroacoustic efficiency of around 70%. Usually, the generation of coherent radiation was achieved by designing a stepped geometry to the radiating profile of the plate [5]. Steps, with a height size of a half-wavelength in the propagation medium, were required at the nodal lines of the plate. Media with small wavelengths, such as air, allow an affordable step performance, but step sizes required for media with much larger wavelengths, such as water, makes it impractical to design a stepped radiator. To address this, a reflector structure was added to the flat rectangular plate transducer. These reflectors were placed at a 45 degrees angle with respect to the two parallel vibrating surfaces of the rectangular plate to duplicate the radiating surface of the transducer. Thus, the acoustic energy emitted from both sides of the radiator was taken advantage of to obtain the desired effects of a coherent acoustic field, also increasing the electroacoustic efficiency of the system. The reflector structure is composed of a system of channels capable of putting in phase the radiation of different zones of the flat rectangular plate that vibrate in counter-phase. The effect of this structure is shown in Fig. 2. The ultrasonic field generated by the internodal sectors of the plate, vibrating in a flexural mode, propagates in counter-phase to the reflectors, as can be observed in Fig. 2a. The channels structure is capable of putting in phase the ultrasonic waves after the first reflection, and subsequently transmitting a coherent field in free field: As mentioned before, the mechanical amplifier has been lengthened λ/2 in the narrow section because the protective housing of the transducer may interfere with the ultrasonic waves generated by the flat rectangular plate in their path to the reflectors. With this extension, the protective housing remains outside the reflectors system and the interferences are minimized. This can be observed in Fig. 2b, where the narrow section of the horn is 3λ/4 long. The appearance of the whole system is shown in Fig. 3:
Fig. 1. Airborne power ultrasonic transducer with a rectangular plate radiator.
In the following sections, the radiated fields, in the near field, generated by this new APUT system will be presented and analyzed numerically and experimentally, focusing on the pressure amplitude distribution at different distances and on the directivity patterns obtained in the far field, in comparison with the APUT with flat rectangular plate without the reflectors system. Even if the idea of attaching a reflectors system to an APUT with flat rectangular radiator for a coherent acoustic radiation was presented previously [10], this is the first time that the acoustic behavior of such system has been numerically and experimentally analyzed with the radiator vibrating in a complex flexural mode, thus validating a numerical model for this system. The results obtained after this analysis confirm that the system of reflectors allows coherent radiation, compared to the APUT with flat rectangular transducer without reflectors. 2. Description of the ultrasonic system The APUT described in [11] basically consists of a piezoelectric Langevin-type sandwich including four stacked piezoceramic rings, prestressed at 25 MPa, a half-wavelength mechanical amplifier (horn); and an extensive flat radiator with rectangular geometry that allows a good impedance match with the gas medium and a high-intensity ultrasonic field. Fig. 1 shows the airborne power ultrasonic transducer. The desired operational mode of the transducer corresponds to an extensional mode of the ultrasonic vibrator (Langevin-type sandwich and horn) which drives the radiator into resonance in one of its flexural modes. In the present study the plate radiator vibrates in a flexural
3. Acoustic field generated by this new system 3.1. Numerical simulation of the ultrasonic field The determination of the acoustic field generated by this ultrasonic system can be carried out using numerical and experimental methods. The numerical determination of the ultrasonic field has been calculated using FEM methods with the simulation software COMSOL Multiphysics®. The numerical analysis of the ultrasonic transducer with
Fig. 2. Food dehydration system with an APUT and a reflector system. 2
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Fig. 3. Two views of the ultrasonic system with reflectors.
a rectangular flat plate radiator has already been presented in [11], where the operational mode with twelve nodal lines (12|0) has been found at 21,049 Hz. The ultrasonic field generated by this transducer can be obtained with a multiphysics simulation in which the structural mechanics module simulates the vibration of the rectangular radiator, and the acoustics module simulates the ultrasonic field. The displacements that take place in the surface of the radiator excite the particles of the fluid creating an acoustic wave that propagates along the fluid domain. The processing capacity of the computer is critical when carrying on FEM simulations, especially in the case of 3D simulations. The basis of the finite element method is that, when it is necessary to solve an equation in a certain domain, this domain can be divided into small elements in which the equation can be easily solved, and the solution for each element can be used as a boundary condition for the next one. This process requires that the size of each element to be as small as possible in order to insure a good convergence of the solution. Therefore, the smaller the size of each element, the larger the number of elements, and the higher the required processing capacity of the computer. Shannon’s sampling theorem leads to the idea of using a fixed amount of elements per wavelength. In [13], an analysis of the error obtained for a different type of elements and the number of elements per wavelength is presented. In the case of quadratic elements, and for a long duct filled with air, the conclusion obtained in [13] was that two elements per wavelength correspond to an error of about 10 percent. Therefore, it is recommendable to have at least two quadratic elements per wavelength. In this case, the transducer is vibrating at 21,049 Hz in air, meaning that the ultrasonic waves have a wavelength around 16 mm (considering that the sound speed in air is 343 m/s). According to this, the maximum size of the elements should be 8 mm, even though smaller elements are used. The fluid where the acoustic propagation is simulated is air at 20 °C, considered a linear elastic fluid, in which thermoviscous losses are considered negligible. The equation solved in the FEM model corresponds to the linear wave equation (Eq. (1)) in a lossless medium [14]:
·
1
p
2p =0 c2
simulation may be quite large, depending on the size of the domain and the frequency of the wave. In this case, 2D and 3D simulations have been carried out for the ultrasonic field generated by the flat rectangular plate transducer, which is excited with a monochromatic continuous wave at around 21 kHz, in order to induce the desired flexural mode with twelve nodal lines. The transducer can be observed in Fig. 1. A schematic representation of the transducer is depicted in Fig. 4a, with the operational mode (12|0) presented in Fig. 4b: In the case of a rectangular piston, the identification of the near field and the far field could be done theoretically using the Rayleigh distance which, for plane radiators acting as a piston, can be determined using Eq. (2) [15]:
D=
2 fa2 2c
(2)
In Eq. (2), a is half of the largest dimension of the radiator, f is the propagation frequency and c represents the sound speed in the medium. The separation between the near field and the far field is located at a distance of 1/π of the Rayleigh distance. This theoretical equation is suitable for a rectangular piston. According to Eq. (2), the Rayleigh distance of a rectangular piston with these dimensions is 15.7 m, meaning that the separation between the near and far field is located at approximately 5 m from the source. However, the transducer is not acting as a piston because it vibrates in a flexural mode, and the previous calculation should be considered as a mere reference. In order to set an approximate frontier between a hypothetic near field and far field, a 2D numerical determination has been done, obtaining the ultrasonic field in the plane XY, with a maximum element size of /6, to delimit the size of the 3D simulation to an area near the transducer, with a pressure distribution similar to the one of an ideal piston. The simulations are done considering free field propagation, by defining Perfectly Matched Layers (PML’s) in the boundaries of the fluid domains. The 2D simulation allows a larger distance with a higher resolution because the number of elements, thus the required computational resources, is much smaller than in a 3D simulation. The result of this analysis can be observed in Fig. 5. The acoustic field is generated by the transducer vibrating at its operational mode with 12NL at a frequency of 20,481 Hz. A simulated continuous wave excitation of 200 W is shown in Fig. 5a and the acoustic pressure evolution along the x-axis is shown in Fig. 5b: As can be observed in Fig. 5b, the pressure amplitude distribution along the axis approximately follows the pressure distribution of the acoustic field generated by a piston [12], with an alternation of maxima and minima of pressure amplitude near the radiator, and a progressive amplitude decrease further away. The pressure distribution of the rectangular plate transducer, under the defined operational conditions,
(1)
where p is the acoustic pressure, and c are the density and sound speed of the fluid and represents the angular frequency of the wave. 3.1.1. Numerical simulation of the acoustic field generated by a flat rectangular plate transducer vibrating in a flexural mode As mentioned before, the computational resources required in a 3D 3
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Fig. 4. (a) Schematic representation of the transducer. (b) Operational mode with 12 nodal lines around 21 kHz.
shows an alternation of maxima of pressure up to one meter from the transducer, and an amplitude decrease after that distance, but this decrease is not really progressive because other areas with maxima appear. The limit between an area considered as near field and the far field can be set, in this situation, at about one meter from the radiator. The 3D simulation comprises a length of 1.2 m in order to cover the area of interest. This 3D simulation allows the possibility of obtaining 2D slices parallel to the surface of the radiator, in order to view the acoustic evolution in the near field (Fig. 6): Fig. 6 shows pressure nodes affected by the nodal lines of the radiator, and how the pressure map becomes more homogeneous when
the distance from the radiator is increased. Two areas with maximum pressure values appear in Fig. 6f, corresponding to the YZ slice at a distance of 968 mm from the transducer. The energy focuses on these areas, resulting in two directional lobes. These lobes can be observed in Fig. 7 and in the directional patterns presented in section 4, and also in Fig. 21b: 3.1.2. Numerical simulation of the acoustic field generated by the ultrasonic system with reflectors The numerical simulation of the acoustic field generated by the ultrasonic system with reflectors has been carried out in a 3D model.
Fig. 5. 2D numerical simulation of the acoustic field generated by a flat rectangular APUT vibrating at its operational mode at 20,481 Hz. (a) Ultrasonic field in the XY plane. (b) 1D continuous wave axial pressure variations. 4
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Fig. 6. Slices in the YZ plane, parallel to the flat radiator, at different distances.
Fig. 7. Acoustic pressure (Pa) amplitude distribution in the plane XZ.
computational resources, a two-step simulation has been done, obtaining the amplitude pressure map at the output of the SWR in the first step, and using this result as an input in the second step, the free field simulation. The axis orientation in this simulation is shown in Fig. 8: As mentioned before, the first simulation tries to determine the nature of the ultrasonic field generated by a virtual radiator that would be the output of the ultrasonic system, which corresponds to the YZ plane in Fig. 8. The operational mode of the rectangular plate transducer has a shape with 12 nodal lines (12|0), at a frequency of 20,481 Hz. In order to reduce the computational resources required to do this simulation, and taking into account that the model is symmetric, only a quarter of the system has been analyzed, applying symmetric boundary conditions and rebuilding the whole model for presentation purposes. The first step consists of the determination of the ultrasonic field at the output of the SWR, which is the amplitude pressure field of the virtual radiator. The acoustic field inside the reflectors system and at the output is presented in Fig. 9: The pressure amplitude distribution presented in Fig. 9b is introduced as an initial value for the free field simulation, in order to determine the acoustic field generated by the whole system. This acoustic field, determined numerically under free field conditions, is presented in Fig. 10, where the XY plane and the XZ plane are shown:
Fig. 8. Schematic representation of the system with reflectors.
The computational resources required in this simulation are higher because it is necessary to simulate two acoustic fields, the field obtained in the space between the transducer and the reflectors, and the field that the system generates into the free field. In order to reduce these 5
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Fig. 9. (a) Ultrasonic field inside the reflectors system. (b) Acoustic pressure in the virtual radiator.
On the other side, YZ planes, parallel to the virtual radiator are also presented in Fig. 11 to view the acoustic evolution near the radiator: Comparing the pressure distribution obtained with the flat rectangular plate (Figs. 5–7) and the pressure distribution obtained with the
ultrasonic system (Figs. 10 and 11), it can be seen that the latter doubles the area of interest, and that there are higher pressure amplitudes in the free field. This event is produced by constructive interferences that occur after putting in phase the acoustic waves with the reflectors.
Fig. 10. Acoustic pressure (Pa) distribution under free field conditions, generated by the ultrasonic system with reflectors.
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Fig. 11. Slices in the YZ plane, parallel to the radiation surface of the system with reflectors, at different distances.
The experimental analysis will confirm the improvements obtained with the SWR and will validate the numerical model used in these simulations.
continuously along the axis in order to first identify the limit between the near and far field, and then determine the location of maximum pressure amplitude points in the near field. The acoustic pressure amplitudes were determined from the voltage measurements, taken with a spatial resolution of 1 mm associated with the limitations of the measuring setup. Then, 2D raster scans were carried out in planes parallel to the radiating surface of the transducer where the maxima in the near field are located. In these scans, sweeps cover the desired plane, with continuous displacements along the y-axis, and steps of 1 mm in the z-axis. Pressure measurements in planes perpendicular to the transducer emitter surface have been obtained with 2D Raster scans with a continuous movement along the y axis and 1 mm steps in the x axis. The experimental setup is composed by an ultrasonic controller, whose task is to drive the transducer into the desired operational mode and track this mode even if the working frequency varies. The signal goes to an impedance matching unit through the amplifier and then to the transducer, which vibrates at the required frequency and generates the ultrasonic field that is measured as explained before. The electrical output of the microphone registered at each point is stored on a PC. The output voltage level from the microphone is then converted to the equivalent acoustic pressure (Pa), using the sensitivity of the microphone (1 mV/Pa). The block diagram of the measurement setup is shown in Fig. 12: As mentioned before, the experimental determination of the ultrasonic pressure amplitude field has been done in a semi-anechoic chamber, with dimensions 5 × 3,3 × 3,5 m3 (57,75 m3). The semi-anechoic chamber has a reflecting floor and absorbing enclosures, as can be observed in Fig. 13:
3.2. Experimental setup for the ultrasonic field determination The ultrasonic field generated under operational conditions is intended to have a sound pressure level higher than 150 dB at the operational frequency around 21 kHz. An electric supply between 150 W and 200 W is necessary to produce such a high pressure level, and should be the operational power supply. Nevertheless, this sound pressure level is very high even for the measurement transducer (microphone GRAS 40DP), which is not capable of withstanding such extreme amplitudes. This comes about because this type of condenser microphones have a membrane that reacts to the incident acoustic pressure by moving back and forth, and as a result, the capacitance of the condenser analogously to the frequency and amplitude of the sound wave changes. If the acoustic pressure amplitude is as high as 150 dB, this thin membrane may break and result in the failure of the microphone. For this reason, a linear approximation has been done in the experimental determination of the acoustic field generated by the rectangular plate transducer and by the SWR. The excitation level in all cases has been 20 W. The experimental characterization of the acoustic pressure amplitude field generated by the APUT with flat rectangular plate both with and without a reflector system has been carried out in a hemi-anechoic chamber, where a PC-controlled 3D measuring system was used. The X, Y, Z coordinates related to the microphone position are governed by means of numerical control equipment (Labview® code), and they are sent to an analog treatment stage. 2D raster scans, which measure the SPL, have been done with a 1/8″ pressure microphone (GRAS 40DP), capable of measuring low frequency ultrasound. The measuring process consists of an initial 1D scan along the axis normal to the surface of the transducer with the microphone moving
3.2.1. Ultrasonic field generated by the flat rectangular plate transducer without reflectors This first determination is the ultrasonic field generated by the transducer without the reflectors system, shown in Fig. 1, and with the axis orientation represented in Fig. 4. Firstly, a 1D linear scan along xaxis allows the location of the maximum and minimum values that 7
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Fig. 12. Block diagram for the ultrasonic field experimental setup.
appear in the near field. In Fig. 14, all these distances are identified. The x-axis represents the separation to the plate, and the y-axis represents the microphone response in volts, analogous to the sound pressure amplitude obtained at each point: The limit between the near and far field appears at 1129 mm from the radiator. In the near field, there are six distances that correspond to maximum values of pressure amplitude (38 mm, 131 mm, 300 mm, 478 mm and 601 mm). As mentioned before, the measurements have
been done for an excitation of 20 W. The slices, in plane YZ, parallel to the surface of the plate, at each distance, are shown in Fig. 15: The nodal lines can be easily observed, as the measurements are taken in the near field, although they are losing resolution because of the spherical propagation of the waves. The last figure corresponds to the limit between the near and far field, with a more homogeneous field in the slice. The ultrasonic field in the planes XY and XZ (Fig. 16) are also
Fig. 13. Semi-anechoic chamber where the experimental ultrasonic field determination has been done.
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Fig. 14. Ultrasonic field along the axis of the radiator of the transducer without reflectors.
Fig. 15. 2D ultrasonic field in the plane YZ at different distances from the radiator without reflectors.
described. The maxima and minima are perfectly identified in the near field, and also the uniformity in the far field, but with much lower amplitude due to the air absorption at 21 kHz and spherical propagation of ultrasonic waves: As can be observed in Figs. 5–7; and in Figs. 15 and 16, the numerical simulation and the experimental determination show a good correlation, validating the model used in this case.
orientation is shown in Fig. 8, and the identification of the near and far field is represented in Fig. 17: The limit between the near and far field appears at 2612 mm from the radiator. In the near field, there are four distances that correspond to maximum values of pressure amplitude (0 mm, 248 mm, 419 mm, 549 mm, and 1083 mm). The slices, in plane YZ, parallel to the surface of the plate, at each distance, are shown in Fig. 18: The ultrasonic field is more uniform after putting the ultrasonic waves in phase. The central line that appears for X = 0 corresponds to a surface of the radiator. The field becomes more homogeneous when moving away from the surface. The field in the planes XY and XZ has been also determined (Fig. 19). The results obtained after the experimental determination reflect
3.2.2. Ultrasonic field generated by the ultrasonic system with reflectors Using the same methodology applied in the previous section, the ultrasonic pressure amplitude field generated by the SWR has been described. In this case, the radiating surface considered has been the coherent field coming out of the structure once the ultrasonic waves have reflected in the structure and have been put in phase. The axis 9
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Fig. 16. 2D ultrasonic field in the perpendicular planes to the transducer’s radiation surface. (a) Plane XY. (b) Plane XZ.
the improvements obtained when using the reflectors, confirming the expectations which resulted from in the numerical analysis.
order to improve the versatility of the transducer and to double the efficiency of the system (using both faces of the radiator), this system with reflectors was developed. The directivity measurements have been done in an anechoic room located in the facilities of the Instituto de Tecnologías Físicas y de la Información “Leonardo Torres Quevedo”, CSIC, in Madrid (Spain). This chamber has operational dimensions of 7.5 × 5.5 × 5.5 m3. The cut-off frequency is 80 Hz, so the chamber behaves as a free field above that frequency. All the enclosures of the chamber are covered with wedges made of mineral wool, in order to maximize the absorbing surface inside the chamber. The acoustic
4. Directivity of this new system The main objective of the ultrasonic SWR is to generate coherent ultrasonic radiation in free field. Usually, the application of steps in the surface of the radiator is essential in the generation of a coherent field [5], nevertheless, only the energy generated by the radiating surface is used, neglecting the energy radiated by the rear face of the plate; and, as mentioned before, plates with steps built in are not very versatile. In
Fig. 17. Ultrasonic field in the axis normal to the radiating surface of the system with reflectors. 10
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Fig. 18. 2D ultrasonic field in the plane YZ at different distances from the radiating surface of the system with reflectors.
Fig. 19. 2D ultrasonic field in the perpendicular planes to the radiation surface of the ultrasonic system with reflectors. (a) Plane XY. (b) Plane XZ.
properties of the chamber satisfy the requirements indicated in the Annex A of the Spanish standard UNE-EN-ISO 3745:2012: “Acoustics - Determination of sound power levels and sound energy levels of noise sources using sound pressure - Precision methods for anechoic rooms and hemi-anechoic rooms”, with the general procedure for the qualification of anechoic and hemi-anechoic rooms. The anechoic chamber can be observed in Fig. 20: The measurements were done with a 1/8″ pressure microphone (GRAS 40DP) placed at a distance of 7.8 m, in the far field. The
measurement setup is similar to the one described in the ultrasonic field characterization (Fig. 12), for a low power excitation (20 W). The emitter in each case was bolted to a rotating structure capable of pivoting in steps of one degree in order to measure the acoustic pressure generated by the emitter in a sector of 180°. The directivity of each system has been determined for the planes XY and XZ, following the directional specifications shown in Figs. 4 and 8, respectively. The results obtained after the measurement campaign are shown in Fig. 21. 11
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Fig. 20. Anechoic chamber for the directivity determination of the system without and with reflectors.
Fig. 21. Directivity of the two ultrasonic systems. (a) Flat rectangular plate, plane XY, horizontal direction. (b) Flat rectangular plate, plane XZ, vertical direction. (c) Ultrasonic system with reflectors, plane XY, horizontal direction. (d) Ultrasonic system with reflectors, plane XZ, vertical direction. 12
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The ultrasonic SWR shows a very directional behavior (Fig. 21c and d), similar to a piston, while the directivity of the transducer without SWR presents two main lobes with angles around 10° and −10° with the normal direction in the horizontal plane (XY plane).
dehydrated, environmental conditions (temperature, humidity), or the use of airflow in the process.
5. Conclusions
This work has been supported by the project DPI2012-37466-C0301 funded by the Spanish Ministry of Economy and Competitiveness. We would like to thank Mr. Ángel Guinot for his kind assistance during the measurement campaigns in the acoustic chambers, for the determination of the acoustic field and directivity pattern of the two systems analyzed.
Acknowledgments
An APUT with rectangular radiator for airborne applications has been numerically designed, developed and experimentally validated at low power conditions. The active part of this system, the transducer, has a very high quality factor (Q ≈ 13,000), a narrow bandwidth (1.59 Hz), an electroacoustic efficiency of about 80% and a resonance frequency around 21,100 Hz. A system with reflectors has been attached to the airborne power ultrasonic transducer as a new system to increase the global efficiency of the system and to generate coherent ultrasonic radiation in free field, putting in phase the ultrasonic waves generated by the transducer. The acoustic behavior of the whole system has been analyzed by numerical and experimental means. The numerical analysis has been done using the FEM software COMSOL Multiphysics®. The simulation shows an acoustic field with higher pressure amplitude in a wider area of interest when using the reflectors system. The experimental determinations have validated the numerical models and have confirmed the expected behavior of both configurations. These determinations have been done with two different experiments for the APUT without and with reflectors: a measure of the ultrasonic field in a semi-anechoic chamber and the directivity determination in an anechoic room. Our experimental results demonstrate for the first time the ability to use reflecting structures coupled to high power transducers to generate intense and coherent acoustic fields. The planar sheet-steps of these structures are mechanically attached to the planar displacement nodes of the vibrating surface of the plate, producing a coherent field. Our whole ultrasonic system, including the reflectors, shows a high directivity, concentrating the acoustic energy in the axial direction, while the system without reflectors radiates the acoustic energy forming 10° angles with the axis. This new system provides versatility for the actuation of plate-based transducers as these structures can be modified or replaced by others depending on the mode of vibration selected for each specific desired application. Future research lines will test the performance of this ultrasonic system in real food dehydration experiments under different operational conditions such as the nature of the food samples to be
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