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Contactless Liquid Height and Property Estimation Using Surface Acoustic Waves

Contactless Liquid Height and Property Estimation Using Surface Acoustic Waves acoustics Article Contactless Liquid Height and Property Estimation Using Surface Acoustic Waves 1 , 2 2 , Hani Alhazmi and Rasim Guldiken * Mechanical Engineering Department, Umm Al-Qura University, Makkah 21955, Saudi Arabia; haalhazmi@mail.usf.edu Mechanical Engineering Department, University of South Florida, Tampa, FL 33620, USA * Correspondence: guldiken@usf.edu; Tel.: +1-813-974-5628 Received: 24 April 2020; Accepted: 4 June 2020; Published: 6 June 2020 Abstract: The propagation of surface acoustic waves over a solid plate is highly influenced by the presence of liquid media on the surface. At the solid–liquid interface, a leaky Rayleigh wave radiates energy into the liquid, causing a signification attenuation of the surface acoustic wave amplitude. In this study, we take advantage of this spurious wave mode to predict the characteristics of the media, including the volume or height. In this study, the surface acoustic waves were generated on a thick 1018 steel surface via a 5 MHz transducer coupled through an angle beam wedge. A 3D-printed container was inserted on the propagation path. The pulse-echo time-domain responses of the signal were recorded at five di erent volumes (0, 400, 600, 1000, and 1800 L). With the aid of parametric CAD analysis, both the position and distance of the entire traveling wave in the liquid layer were modeled and verified with experimental studies. The results indicated that the average drop in the reflected wave amplitude due to liquid loading is 62.5% compared to the empty container, with a percentage of error within 10% for all cases. The localized-time frequency components of the reflected wave were obtained via a Short-Time Fourier Transform technique. Up to 10% reduction (500 KHz) in the central frequency was observed due to the liquid volume increasing. The method discussed herein could be useful for many applications, where some of the liquid’s parameters or the ultrasonic wave behavior in the liquid need to be assessed. Keywords: surface acoustic wave; attenuation; leaky Rayleigh wave; Short-Time Fourier Transform Analysis 1. Introduction Surface acoustic waves (SAWs) have been widely utilized to detect surface defects in many structural health monitoring applications. The propagation of SAWs over a thick solid plate is highly influenced by the presence of liquid on the surface. Therefore, the estimation of the defect location or depth can be inaccurate since the output signal includes additional wave packets, which is caused by the presence of liquid on the surface. In this study, we take advantage of these spurious wave packets to understand the characteristics of the liquid media. At the solid–liquid interface, a leaky Rayleigh wave is actuated, which radiates energy into the liquid, causing a signification drop in the SAW amplitude [1–3]. Due to the di erence in the acoustic impedance between the solid and liquid at the interface, a refracted longitudinal wave propagates into the liquid layer until it hits the liquid–air boundary and returns to the solid surface. The theory of elastic wave propagation along an interface between two media has been well studied. For instance, Stonely solved the wave propagation along a solid–solid interface (Stoneley’s waves) [4], whereas Scholte studied the wave propagation along a solid–liquid interface (Scholte’s waves) [5,6]. The Rayleigh wave and leaky Rayleigh wave at the solid–liquid interface were studied [6]. Acoustics 2020, 2, 366–381; doi:10.3390/acoustics2020021 www.mdpi.com/journal/acoustics Acoustics 2020, 2 367 The leaky Rayleigh wave exists at the interface when the longitudinal velocity of the liquid is smaller than the shear wave velocity in the solid half-space [7,8]. The propagation of surface waves along the solid–liquid interface, where the liquid velocity is higher than the shear velocity in the solid, was investigated theoretically and experimentally by Padilla for the existence of a surface wave at a plastic–liquid interface [9]. The multiple pulsed leaky Rayleigh wave component propagation in the liquid layer over an aluminum plate was experimentally studied, and the velocity of the pulsed leaky Rayleigh wave was found to be higher than the Rayleigh wave velocity, while the amplitude of the pulsed leak Rayleigh components was increased [1]. SAW (or Rayleigh wave)-based devices, which are typically made of anisotropic materials such as LiNbO , where the SAW characteristics depend on the orientation, have gained considerable attention [10]. The sensitivity of SAWs to liquid-loading on the SAW devices has led to a wide range of applications such as liquid shear viscosity measurement [11], glycerin concentration sensing in a microfluidic channel [12], early ovarian cancer detection [13,14], particle and cell separation [15–17], and liquid mixing and pumping in microchannels [18,19]. Other useful applications of SAWs are quantifying cell growth [20], quantifying bolt tension in bolted joints [21,22], and pH sensing in cultures [23]. By contrast, only a few applications have taken advantage of the e ect of liquid-loading over a solid material (isotropic) on SAWs. One possible application would be estimating liquid height using SAWs. In literature, there are a couple of methods for determining liquid height via using a single or multiple ultrasonic transducer(s), where the basic principle works on the discrepancy in the acoustic impedance of the two media. In one of the studies, the liquid height was measured utilizing two ultrasonic transducers coupled to a tank wall. The first transducer transmits the bulk shear wave that propagates along the solid member in a zigzag path, and the second transducer receives the reflected wave from the solid–liquid interface. Based on the attenuated amplitude of the signal, the acoustic impedance of the liquid can be measured [24]. A non-contact ultrasonic PING sensor was utilized to measure water height with the aid of a microcontroller to calculate the change in the arrival times of the echoes from water [25]. Another method measured liquid height by utilizing three transducers; one transmitter was located between the two echo receiving transducers, and these transducers were encapsulated to overcome the coupling issue. The measurement was achieved by moving the transducers along the container wall, and a noticeable di erence in the reflected wave energy was observed when the transmitter moved from the above liquid level to the below liquid level [26]. The advantages of employing SAWs in detecting surface flaws are that they propagate close to the free surface of a specimen, are easy to excite and record, and are less complicated compared to other types of ultrasonic waves [27–29]. The proposed method to measure fluid height via SAWs is simple, fast, and inexpensive. Moreover, the proposed methodology has the capability to measure a small amount of fluid on a solid surface, such as a spill from a distance, with a small error. The measurement can be achieved by exciting the SAW through an o -shelf piezoelectric transducer connected to the angle beam wedge. The wave reflected from the liquid propagates back towards the transducer, and the received signal is recorded via an oscilloscope. Performing a thorough analysis of the time domain response of the received signal determines the arrival time of the leaky Rayleigh wave from the solid–fluid interface and the arrival time of the reflected wave from the top surface of the fluid. In the final step, a height equation that is derived from Snell’s law and the fluid proprieties can be utilized to accurately find the height. There are two primary aims of this study. The first goal is to investigate the e ect of liquid loading on the propagating SAWs over a solid surface and how the reflected wave from a defect changes due to the existence of liquid media in the propagation path. The second aim is to investigate the capability of measuring the liquid level that is present on the specimen’s surface via SAWs. Understanding how a liquid influences the SAW signal is essential when the SAWs are utilized in a structural health-monitoring application. It is also vital to estimate the liquid properties if the height and surface parameters are known. Acoustics 2020, 2 368 Acoustics 2020, 2, 366–381  368 of 381  2. Methodology 2. Methodology  2.1. Operation Principle 2.1. Operation Principle  When the surface acoustic wave (SAW) arrives at the first point of contact between the liquid When the surface acoustic wave (SAW) arrives at the first point of contact between the liquid  and solid surface, some energy radiates into liquid due to the di erence in the acoustic impedance and solid surface, some energy radiates into liquid due to the difference in the acoustic impedance  between the two media. The acoustic impedance strongly depends on the density and velocity of between the two media. The acoustic impedance strongly depends on the density and velocity of the  the medium, where the density is much higher in solids than in liquids. medium, where the density is much higher in solids than in liquids.  Z = c (1) 𝑍 𝑐𝜌   (1) 2 2 3 3 where Z is the acoustic impedance (rayl/m ),  is the density of medium (kg/m ), and c is the sound  where Z is the acoustic impedance (rayl/m ),  is the density of medium (kg/m ), and c is the sound speed through the material (m/s). The reflection coefficient can be expressed in Equation (2):  speed through the material (m/s). The reflection coecient can be expressed in Equation (2): 𝜌 𝐶 𝜌 𝐶 C  C 𝑅   2 2 1 1 (2) R = (2) 𝜌 𝐶 𝜌 𝐶 C +  C 1 1 2 2 Along the liquid–solid interface, the wave propagates as a leaky Rayleigh wave (LRW) with a  Along the liquid–solid interface, the wave propagates as a leaky Rayleigh wave (LRW) with higher  velocity  compared  to  the  SAW  (Rayleigh  wave),  and  its  amplitude  decays,  since  energy  a higher velocity compared to the SAW (Rayleigh wave), and its amplitude decays, since energy continues radiating into the liquid [1–3]. Due to the difference in the speed of sound between the  continues radiating into the liquid [1–3]. Due to the di erence in the speed of sound between the liquid liquid and leaky Rayleigh wave, the wave at the interface is refracted from the solid to the liquid at  and leaky Rayleigh wave, the wave at the interface is refracted from the solid to the liquid at angle angle θ1 with respect to the normal axis. Besides, the shear wave cannot be supported in the liquid  with respect to the normal axis. Besides, the shear wave cannot be supported in the liquid layer [29]. layer [29].  The leaky Rayleigh wave velocity, which depends on the types of the two materials at the interface, The  leaky  Rayleigh  wave  velocity,  which  depends  on  the  types  of  the  two  materials  at  the  can be found through experimentation. For example, the speed of sound was experimentally measured interface,  can  be  found  through  experimentation.  For  example,  the  speed  of  sound  was  for the air–aluminum interface as 2964 m/s, whereas the SAW for aluminum is 2952 m/s [1]. In this study, experimentally  measured  for  the  air–aluminum  interface  as  2964  m/s,  whereas  the  SAW  for  we experimentally obtained the leaky Rayleigh wave velocity, which is presented in the experiment aluminum is 2952 m/s [1]. In this study, we experimentally obtained the leaky Rayleigh wave velocity,  results section. which is presented in the experiment results section.  The refraction angle  can be estimated by substituting the longitudinal wave velocity of The  refraction  angle θ1  can  be  estimated  by  substituting  the  longitudinal  wave  velocity  of  deionized water (C ), the leaky Rayleigh wave velocity (C ), and the propagation angle of the SAW Lw LR deionized water (CLw), the leaky Rayleigh wave velocity (CLR), and the propagation angle of the SAW  ( ) into Snell’s law (see Appendix A). (θR) into Snell’s law (see Appendix A).  Once the refracted wave in the liquid reaches the liquid–air boundary, it is reflected with angle Once the refracted wave in the liquid reaches the liquid–air boundary, it is reflected with angle  with respect to the normal axis at the interface due to the large di erence in the speed of sound θ2 with respect to the normal axis at the interface due to the large difference in the speed of sound for  for the two media. Hence, no refraction occurs into the air, and Snell’s law can no longer be satisfied. the two media. Hence, no refraction occurs into the air, and Snell’s law can no longer be satisfied. The  The critical incident angle of liquid can be obtained by substituting  = 90 and C and C into air Lw air critical incident angle of liquid can be obtained by substituting θair = 90° and CLw and Cair into Snell’s  Snell’s law (see Appendix A). law (see Appendix A).  If the incident angle from the liquid is higher than the critical angle, the wave will be reflected If the incident angle from the liquid is higher than the critical angle, the wave will be reflected  entirely at the liquid–air interface, as illustrated in Figure 1a. If the incident angle from the liquid is entirely at the liquid–air interface, as illustrated in Figure 1a. If the incident angle from the liquid is  equal to the critical angle, the refracted wave travels parallel to the interface between the air and liquid, equal to the critical angle, the refracted wave travels parallel to the interface between the air and  as shown in Figure 1b. In this study, as the  >> c , the wave will be reflected with angle  , 1 ritical 2 liquid, as shown in Figure 1b. In this study, as the θ1 >> critical, the wave will be reflected with angle  which is equal to  , as illustrated in Figure 1a. θ2, which is equal to θ1, as illustrated in Figure 1a.  (a)  (b)  Figure 1. (a) Schematic representation of a wave traveling in the liquid when the reflected angle at the solid–liquid Figure 1. (a) Schematic representation of a wave traveling in the liquid when the reflected angle at the  solid–liquid interface is larger than the critical angle; (b) Schematic representation of a wave traveling  in the liquid when the reflected angle at the solid–liquid interface is equal to the critical reflected  angle.  Acoustics 2020, 2 369 Acoustics 2020, 2, 366–381  369 of 381  interface is larger than the critical angle; (b) Schematic representation of a wave traveling in the liquid when the reflected angle at the solid–liquid interface is equal to the critical reflected angle. 2.2. Liquid Height Estimation  2.2. Liquid Height Estimation The liquid height can be estimated by using the arrival time of the leaky Rayleigh wave (tA),  The liquid height can be estimated by using the arrival time of the leaky Rayleigh wave (t ), which occurs at the solid–fluid interface, and the arrival time of the reflected wave from the top A   which occurs at the solid–fluid interface, and the arrival time of the reflected wave from the top surface surface of the fluid (tB). Besides these values, the theoretical speed of sound for the fluid and the  of the fluid (t ). Besides these values, the theoretical speed of sound for the fluid and the refraction refraction angle B  at the interface (θ1) are used in determining the liquid height.  angle at the interface ( ) are used in determining the liquid height. Since the liquid is held 1  in a finite container, two cases are expected to exist, as shown in Figure  Since the liquid is held in a finite container, two cases are expected to exist, as shown in Figure 2. 2. The first case occurs when the propagating wave in the liquid hits the liquid–air boundary and  The first case occurs when the propagating wave in the liquid hits the liquid–air boundary and reflects reflects directly to the solid–liquid interface. By contrast, in the second case, the reflected wave hits  directly to the solid–liquid interface. By contrast, in the second case, the reflected wave hits the container the container edge before reaching the solid–liquid interface. These two cases rely mainly on the ratio  edge before reaching the solid–liquid interface. These two cases rely mainly on the ratio of the liquid of the liquid height to the particular container dimensions. Based on the calculation of incident angle  height to the particular container dimensions. Based on the calculation of incident angle  ,  , θ1,  θ3,  and  the  geometric  dimensions  of  the  container,  the  first  case  occurs  if  the  height 1   is 3  and the geometric dimensions of the container, the first case occurs if the height is approximately in approximately in the range of (0 < h < 0.86 L). By contrast, the second case occurs if the height is higher  the range of (0 < h < 0.86 L). By contrast, the second case occurs if the height is higher than 0.86 L. than 0.86 L.      (a)  (b)  Figure Figure 2. 2. (a (a) )Sche Schematic matic representation representation ofof a wa a wave ve traveling traveling  at a at different a di erent  leve level l of li of qui liquid, d, inclu including ding the  critica the critical l case case, , whiwhich ch occurs occurs  at hat < h0.< 860.86  L (first L (first  case case); ); (b) Schem (b) Schematic atic representation representation  of a of wave a wave  traveling traveling  in  the in the  liqu liquid id whe when n the the  liqu liquid id height height  is higher is higher  than than  0.86 0.86  L (c La(case se 2).2).   The total distance the propagating wave travels in the media is S + S as illustrated in Figure 2a. The total distance the propagating wave travels in the media is S 11 + S2, 2, as illustrated in Figure 2a.  S and S are the distances traveled by the incident wave from the solid–liquid interface (upward) S1 1 and S22 are the distances traveled by the incident wave from the solid–liquid interface (upward)  and liquid–air interface (downward), respectively, and L is the actual length of the container. Since and liquid–air interface (downward), respectively, and L is the actual length of the container. Since  the incident angle from the liquid ( ) and the reflected angle at the liquid-air interface ( ) are equal, the incident angle from the liquid (θ1 1) and the reflected angle at the liquid‐air interface (θ2 2) are equal,  S = S . For the experimental tests, the total distance traveled by a propagating wave in a medium can S1 1 = S2. 2 For the experimental tests, the total distance traveled by a propagating wave in a medium can  be expressed as: be expressed as:  S + S = C  (t t ) (3) 1 2 Lw B A 𝑆 𝑆 𝐶 𝑡 𝑡   (3) where t is the arrival time of the reflected wave from the liquid–air interface, and t is the arrival B A where tB is the arrival time of the reflected wave from the liquid–air interface, and tA is the arrival  time of a leaky Rayleigh wave at the solid–liquid interface. For accuracy purposes, both arrival times time of a leaky Rayleigh wave at the solid–liquid interface. For accuracy purposes, both arrival  should be chosen at the same phase. By substituting S = S into Equation (3), we get 1 2 times should be chosen at the same phase. By substituting S1 = S2 into Equation (3), we get  2S = C  (t t ) (4) 1 Lw B A 2𝑆 𝐶 𝑡 𝑡   (4) From the geometry, the liquid height can be determined as: From the geometry, the liquid height can be determined as:  S 𝑆 =   (5 (5)) cos cos𝜃( ) Substituting Equation (4) into Equation (5), we get:  (6) ℎ 𝑡 𝑡 cos𝜃   Acoustics 2020, 2 370 Substituting Equation (4) into Equation (5), we get: Lw h =  (t t )  cos( ) (6) Acoustics 2020, 2, 366–381  B A 1 370 of 381  As As can can be be observed observed frfrom om Equation Equation (6), (6), the the liquid liquid height height isisa afunction  functionof ofC CLw,, the the traveling traveling time time  Lw and the incident angle at the solid–liquid interface. The derivation of the equations for the second case and the incident angle at the solid–liquid interface. The derivation of the equations for the second  can casebe can found  be foin und Appendix  in Appendix A.  A.  2.3. Experimental Setup 2.3. Experimental Setup  The pulse-echo technique is utilized in this study, in which an ultrasonic wave is generated The pulse‐echo technique is utilized in this study, in which an ultrasonic wave is generated and  and received through using only one transducer. The generation of a SAW (Rayleigh wave) that received  through  using  only  one  transducer.  The  generation  of  a  SAW  (Rayleigh  wave)  that  propagates on the free surface of a solid specimen requires using a normal beam transducer, a comb propagates on the free surface of a solid specimen requires using a normal beam transducer, a comb  transducer, or a transducer that is attached to an angle beam wedge placed on the specimen’s surface. transducer, or a transducer that is attached to an angle beam wedge placed on the specimen’s surface.  The purpose of the angle beam wedge is to convert the longitudinal wave generated via the ultrasonic The purpose of the angle beam wedge is to convert the longitudinal wave generated via the ultrasonic  transducer into a Rayleigh wave at the interface between the wedge surface and the specimen’s transducer  into  a  Rayleigh  wave  at  the  interface  between  the  wedge  surface  and  the  specimen’s  surface [30]. Snell’s law should be considered to calculate the appropriate incident angle inside surface [30]. Snell’s law should be considered to calculate the appropriate incident angle inside the  the wedge to achieve the desired angle of SAW propagation (90 ). As illustrated in Figure 3, the angle wedge to achieve the desired angle of SAW propagation (90°). As illustrated in Figure 3, the angle  beam wedge (ABWML-5T 90, Olympus NDT, Waltham, MA, USA) used in this experiment is made of beam wedge (ABWML‐5T 90, Olympus NDT, Waltham, MA) used in this experiment is made of  plastic (Lucite), with a longitudinal wave velocity of 2700 m/s. By substituting the longitudinal velocity plastic  (Lucite),  with  a  longitudinal  wave  velocity  of  2700  m/s.  By  substituting  the  longitudinal  of the wedge and the theoretical Rayleigh wave velocity for a 1018 steel (2953 m/s) into Snell’s law, velocity of the wedge and the theoretical Rayleigh wave velocity for a 1018 steel (2953 m/s) into Snell’s  the incident angle inside the wedge is found to be 66.12 . law, the incident angle inside the wedge is found to be 66.12°.  (a)  (b)  Figure Figure 3. 3. ((aa)) Sc Schematic hematic diagram diagram for for the the expe experiment riment setu setup; p; (b)( bThe ) The  contain container er dimensions dimensions  used u sed in this in  this studstudy y.  . The ultrasonic pulser/receiver (5072PR, Olympus NDT, Waltham, MA, USA) is utilized to excite The ultrasonic pulser/receiver (5072PR, Olympus NDT, Waltham, MA, USA) is utilized to excite  a pulse to a 5 MHz transducer (C541-SM, Olympus NDT, Waltham, MA, USA), which is attached to a pulse to a 5 MHz transducer (C541‐SM, Olympus NDT, Waltham, MA, USA), which is attached to  the angle beam wedge. The received signal can then be amplified before it is transferred to a digital the angle beam wedge. The received signal can then be amplified before it is transferred to a digital  oscilloscope. The amplifier is built in the pulser/receiver, which can be used to control either the gain oscilloscope. The amplifier is built in the pulser/receiver, which can be used to control either the gain  (+dB) or the attenuation (dB) of the received signal. The pulser/receiver has a low pass filter at 10 MHz (+dB) or the attenuation (−dB) of the received signal. The pulser/receiver has a low pass filter at 10  and a high pass filter at 1 MHz. The signal is recorded with 128 averaging to increase the signal-to-noise MHz and a high pass filter at 1 MHz. The signal is recorded with 128 averaging to increase the signal‐ ratio with a digital Oscilloscope (TDS2001C, Tektronix, Beaverton, OH, USA). The sampling time to‐noise ratio with a digital Oscilloscope (TDS2001C, Tektronix, Beaverton, OH, USA). The sampling  time rate was kept constant at 25 μs for the 5 MHz transducer in all recorded signals to avoid aliasing.  The pulser/receiver settings are listed in Table 1.  Acoustics 2020, 2 371 rate was kept constant at 25 s for the 5 MHz transducer in all recorded signals to avoid aliasing. The pulser/receiver settings are listed in Table 1. Table 1. The pulser/receiver settings used during the experimental studies. High Pass Low Pass PRF(Hz) Energy Damping (50 W) Amplifier (Gain) Filter (HPF) Filter (LPF) 100 1 3 1 MHz 10 MHz 30 db The containers were filled with a precise amount of deionized (DI) water via an Eppendorf Research Pipette that can hold 0 to 100 L of liquid. The pipette’s accuracy was verified by dropping 100 L of DI water onto a sensitive scale (Scaout Pro SP402, Ohaus Inc., Parsippany, NJ, USA), and the obtained reading on the scale was used for calibration. The 3D-printed containers, which fit on the specimen’s surface, are made of Polylactic Acid material (PLA). The geometric dimensions of the container are 10 mm  22 mm  8 mm. To measure the actual covered area by the liquid, the container is fully occupied with liquid (2000 mm ) and then the volume is divided by the height of the container (10 mm), which gives the area as 200 mm . The primary purpose of using the container is to maintain the consistency of the area covered by liquid while recording the signal. Initial sets of experiments were conducted to verify that placing the container on the free surface of the specimen had no impact on the propagation of the SAWs. The experiment results confirm that there is no reflection from the containers, since the interface between the specimen’s surface and the container has no real area of contact. The distance between the container and transducer was selected to be 77 mm, which ensured that the container was placed beyond the near field distance (N), which can be estimated using Equation (7). D f N = (7) 4C where D is the transducer diameter, f is the signal frequency, and C is material sound speed. Substituting D = 12.7 mm (0.5 in), f = 5 MHz, and C = 2953 m/s (Rayleigh wave speed) into equation, the near field distance (N) will be 68.27 mm. The material properties for DI water, air, the PLA material, and 1081 steel are listed in Table 2. Table 2. The material properties for deionized (DI) water, air, the PLA material, and 1081 steel. Deionized Water 1018 Steel Air PLA (25 C) Density,  (g/cm ) 1 7.870 0.001 1.24 Speed of Sound (m/s) 1480 2953 (C.R.) 330–343 2200~2300 [31] The experimental procedure is as follows. First, the angle beam wedge is placed on the specimen surface after applying an ultrasonic couplant between the two surfaces to facilitate the ultrasonic wave transmission and reception from the wedge on the specimen surface and vice versa. A three-way C-clamp is used to ensure the wedge remains stationary throughout the experiment and to provide adequate contact between the specimen surface and wedge. Next, the container is placed on the free surface of the specimen (1018 Steel) 77 mm from the wedge tip, whereas the edge is 105 mm from the angle beam wedge. The container area in contact with the specimen is wrapped with a thread sealing tape to prevent the medium from leaking. The reflected signal from the edge for the empty container is selected as the reference for the experimental studies. Thirty seconds after filling the container with DI water, the received signal reflected from the edge of the specimen and the liquid are recorded separately to assist in the data analysis process. The data collection step is repeated for all the di erent liquid volumes investigated. The entire signal for the empty container is shown in Figure 4. It can be observed from this figure that reflection from the wedge-specimen interface is present at 29.2 s in the data, and the reflection from Acoustics 2020, 2 372 Acoustics 2020, 2, 366–381  372 of 381  the specimen edge is at time 99 s. Based on the experimental observation after filling the container Acoustics 2020, 2, 366–381  372 of 381  signal shown on the Oscilloscope, one for the reflection from the specimen edge (RWE) and the other  with liquid, the reflection of the wave from the medium will take place right after 80 s. For better one comparison  for the reflection among al from l cases,  the we liqudecided id (RWL) to as have  show two n in separate  Figurewindows  4.  for the received signal shown signal shown on the Oscilloscope, one for the reflection from the specimen edge (RWE) and the other  on the Oscilloscope, one for the reflection from the specimen edge (RWE) and the other one for one for the reflection from the liquid (RWL) as shown in Figure 4.  the reflection from the liquid (RWL) as shown in Figure 4. Echo from the edge Echo at the  wedge(29.2µs) Echo from the edge Echo at the  wedge(29.2µs) 0 10 203040 5060 708090 100 110 120 ‐1 0 10 203040 5060 708090 100 110 120 ‐2 ‐1 RWF window RWE window ‐3 ‐2 Time(µs) RWF window RWE window ‐3 Time(µs) Figure 4. The entire signal received for the empty container, including the selected windows for the  Figure 4. The entire signal received for the empty container, including the selected windows for reflection from the liquid and the reflection from the edge.  the reflection from the liquid and the reflection from the edge. Figure 4. The entire signal received for the empty container, including the selected windows for the  reflection from the liquid and the reflection from the edge.  3. Results and Discussion  3. Results and Discussion 3. Results and Discussion  3.1. The Effect of the Presence of Liquid Media on the Propagation Path of the Reflected Wave from a Defect  3.1. The E ect of the Presence of Liquid Media on the Propagation Path of the Reflected Wave from (Ed a g Defect e)  (Edge) 3.1. The Effect of the Presence of Liquid Media on the Propagation Path of the Reflected Wave from a Defect  It Itis isimper imperative ative toto stu study dy ho how w the the wa wave ve reflected reflected fro frm om the the ed edge ge is isininfluenced fluenced wh when en a sm a small all area area  (Edge)  ofof a tested a tested  specimen specimen  surfa surface ce is occ is occupied upied by li by quliquid id matter matter  in the in p the roppr agat opagation ion path,path,  mainly mainly  whenwhen  the  It is imperative to study how the wave reflected from the edge is influenced when a small area  medium the medium  is between is between  the transducer the transducer  and the and  defect the to defect  be detected. to be detected.  In generIn al,general,  the amplit theude amplitude  of SAWsof  of a tested specimen surface is occupied by liquid matter in the propagation path, mainly when the  sign SAif Ws icant significantly ly  attenuates attenuates   as  the  lias quthe id  in liquid teractinteracts s  with  thwith e  solid the  (s solid olid–(solid–liquid liquid  interact interaction) ion)  due  to due   theto  medium is between the transducer and the defect to be detected. In general, the amplitude of SAWs  diss theipat dissipation ion of theof signal the signal  energy ener  intgy o the into liqu theid. liquid.   significantly  attenuates  as  the  liquid  interacts  with  the  solid  (solid–liquid  interaction)  due  to  the  The The results results inindicate dicate tha that t the the pea peak-to-peak k‐to‐peak am amplitude plitude ofof the the reflected reflected wave wave from from the the edge edge dec declines lines  dissipation of the signal energy into the liquid.  sharp sharply ly when when 40400 0 μL Lofof DI DI water water is iad s added ded toto the the liq liquid uid container container and and slight slightly ly de decr creases eases oror rema remains ins  The results indicate that the peak‐to‐peak amplitude of the reflected wave from the edge declines  alm almost ost  const constant ant  as as the theliquid   liquid volume   volume incr   incr eases eases (Figur   (Fig eure 5). This   5).  Th indicates is  indithat cates the   tha change t  the  chan in thege amplitude   in  the  sharply when 400 μL of DI water is added to the liquid container and slightly decreases or remains  amplit is mor ude e sensitive  is more sens to the itiv areea tothan  the ar toea the tha liquid n to the volume  liquid pr volume esent in pthe resent propagation  in the prop path. agation path.  almost  constant  as  the  liquid  volume  increases  (Figure  5).  This  indicates  that  the  change  in  the  amplitude is more sensitive to the area than to the liquid volume present in the propagation path.  RWE Empty RWE Empty 94 95 96 97 98 99 100 101 102 103 104 ‐1 Time(µs) 94 95 96 97 98 99 100 101 102 103 104 ‐1 0.6 Time(µs) RWE 400µl 0.4 0.6 RWE 0.2 400µl 0.4 0.2 94 95 96 97 98 99 100 101 102 103 104 ‐0.2 ‐0.4 94 95 96 97 98 99 100 101 102 103 104 Time(µs) ‐0.2 ‐0.4 Figure 5. Cont. Time(µs) Amplitude(V) Amplitude(V) Amplitude(V) Amplitude(V) Amplitude(V) Amplitude(V) Acoustics 2020, 2 373 Acoustics 2020, 2, 366–381  373 of 381  0.6 600µl 0.4 0.2 94 95 96 97 98 99 100 101 102 103 104 ‐0.2 ‐0.4 Time(µs) 0.6 1000µl 0.4 0.2 94 95 96 97 98 99 100 101 102 103 104 ‐0.2 ‐0.4 Time(µs) 0.6 1800µl 0.4 0.2 94 95 96 97 98 99 100 101 102 103 104 ‐0.2 ‐0.4 Time(µs) Figure 5. Time domain response for the reflected wave from the edge for all cases. Figure 5. Time domain response for the reflected wave from the edge for all cases.  The average percentage of the peak-to-peak amplitude drop due to liquid exitance was 62.5%, The average percentage of the peak‐to‐peak amplitude drop due to liquid exitance was −62.5%,  as shown in Table 3. The maximum amplitude of the reflected wave from the edge remains constant as shown in Table 3. The maximum amplitude of the reflected wave from the edge remains constant  in all cases, which occurs at the time of 99.464 s (T ). It is important to note that the wave P-RWE in all cases, which occurs at the time of 99.464 μs (TP‐RWE). It is important to note that the wave reflected  reflected from the defect (edge or corner in this study) was not a ected by the presence of DI water on from the defect (edge or corner in this study) was not affected by the presence of DI water on the  the surface. By utilizing Equation (8)—where v is the theoretical velocity of the Rayleigh wave in surface. By utilizing Equation (8)—where vR is the theoretical velocity of the Rayleigh wave in 1018  1018 steel (2953 m/s) and T is the time associated with the maximum reflection at the angle beam p-wedge steel (2953 m/s) and Tp‐wedge is the time associated with the maximum reflection at the angle beam  wedge, which is 29.2 s—the obtained distance was 103.74 mm, where the actual distance between wedge, which is 29.2 μs—the obtained distance was 103.74 mm, where the actual distance between  the transducer and the edge was 105 mm. The reasonably low 1.9% error herein could be due to the transducer and the edge was 105 mm. The reasonably low 1.9% error herein could be due to the  the theoretical Rayleigh wave velocity or the measurement accuracy. theoretical Rayleigh wave velocity or the measurement accuracy.  T T  v (PRWE) (Pwedge) R Table 3. The percentage drop in the d  = peak‐to‐peak amplitude of the reflected wave from the edge for  (8) all cases.    Empty  400 μL  600 μL  1000 μL  1800 μL  Table 3. The percentage drop in the peak-to-peak amplitude of the reflected wave from the edge for P–P amplitude (V)  1.90  0.74  0.72  0.70  0.70  all cases. 𝑥 𝑒𝑡𝑚𝑝𝑦 % 100   ‐  −61.05 −62.11 −63.16 −63.16  𝑒𝑚𝑝𝑡𝑦 Empty 400 L 600 L 1000 L 1800 L P–P amplitude (V) 1.90 0.74 0.72 0.70 0.70 xempty % =  100 - 61.05 62.11 63.16 63.16 empty 𝑇 𝑇 𝑣 (8)  𝑑   The results further show that wave packets appear before and after the wave reflected from the edge, and they shift to the right as the volume of liquid increases, as shown in Figure 5. These The results further show that wave packets appear before and after the wave reflected from the  edge, and they shift to the right as the volume of liquid increases, as shown in Figure5. These waves  Amplitude(V) Amplitude(V) Amplitude(V) Acoustics 2020, 2 374 Acoustics 2020, 2, 366–381  374 of 381  are  multiple  reflections  from  the  top  surface  of  the  liquid.  The  shift  in  time  occurs  because  the  waves are multiple reflections from the top surface of the liquid. The shift in time occurs because reflected wave travels longer in liquid as the height of liquid increases.  the reflected wave travels longer in liquid as the height of liquid increases. 3.2. The Reflected Wave from the Liquid on the Propagation Path  3.2. The Reflected Wave from the Liquid on the Propagation Path Figure 6 shows the time‐domain responses of the wave reflected from the DI water for all the  Figure 6 shows the time-domain responses of the wave reflected from the DI water for all volumes investigated. Based on observations of the exact location of reflections from the liquid, a  the volumes investigated. Based on observations of the exact location of reflections from the liquid, window between the times of 74 and 98 μs was selected, which covers the region before the RWE. By  a window between the times of 74 and 98 s was selected, which covers the region before the RWE. choosing this window, not only can the first reflected wave from the liquid be easily detected, but the  By choosing this window, not only can the first reflected wave from the liquid be easily detected, behavior  of  the  reflected  signal  can  also  be  precisely  analyzed,  for  example,  the  peak‐to‐peak  but the behavior of the reflected signal can also be precisely analyzed, for example, the peak-to-peak amplitude of the reflected wave from the liquid. During the experiments, we carefully analyzed the  amplitude of the reflected wave from the liquid. During the experiments, we carefully analyzed obtained time‐domain signal of each case. In order to ensure the reflection of the signal was coming  the obtained time-domain signal of each case. In order to ensure the reflection of the signal was coming from the top surface of the fluid, we disturbed the top surface with a needle, and it was observed that  from the top surface of the fluid, we disturbed the top surface with a needle, and it was observed that the amplitude of the reflection died out. The dotted box (A), the dotted box (B), and the dotted box  the amplitude of the reflection died out. The dotted box (A), the dotted box (B), and the dotted box (C) (C) in Figure 6. represent the first leaky Rayleigh wave at the solid–liquid interface at the beginning  in Figure 6. represent the first leaky Rayleigh wave at the solid–liquid interface at the beginning of of the container, the first reflected wave from the top surface of the liquid, and the second leaky  the container, the first reflected wave from the top surface of the liquid, and the second leaky Rayleigh Rayleigh wave at the end of the container, respectively.  wave at the end of the container, respectively. Empty ‐50 74 76 78 80 82 84 86 88 90 92 94 96 98 Time(µs) ‐150 400µl C 74 76 78 80 82 84 86 88 90 92 94 96 98 ‐100 Time(µs) ‐200 600µl 74 76 78 80 82 84 86 88 90 92 94 96 98 ‐100 Time(µs) ‐200 1000µl 100 A ‐50 74 76 78 80 82 84 86 88 90 92 94 96 98 ‐100 Time(µs) ‐150 1800µl 100 B 74 76 78 80 82 84 86 88 90 92 94 96 98 ‐50 Time(µs) ‐100 Figure 6. Time domain responses for the reflected wave from the liquid for all cases. Figure 6. Time domain responses for the reflected wave from the liquid for all cases.  From the results of all the cases, it can be noted that the amplitude of the signal dramatically From the results of all the cases, it can be noted that the amplitude of the signal dramatically  changes when the container is filled with 400 L of liquid around the time of 80.96 s, as seen in changes when the container is filled with 400 μL of liquid around the time of 80.96 μs, as seen in  Figure 6. One can observe that the amplitude of the leaky Rayleigh wave is attenuated as it travels  Amplitude(mV) Amplitude(mV) Amplitude(mV) Amplitude(mV) Amplitude(mV) Acoustics 2020, 2 375 Figure 6. One can observe that the amplitude of the leaky Rayleigh wave is attenuated as it travels along the solid–liquid interface in all cases except one case (400 L). The velocity of the leaky Rayleigh wave at the beginning of the container can be obtained by utilizing Equation (8), where the maximum amplitude occurs at the time of 80.96 s, the actual distance between the transducer and container is 77 mm, and the time at the wedge is 29.2 s. Hence, the velocity obtained is 2975 m/s. The results further show that the first reflected wave from the top surface of the liquid arrives earlier than the first leaky Rayleigh wave in the cases of 400 L and 600 L, whereas it arrives later than the first leaky Rayleigh wave in the case of 1000 L and 1800 L. The reason for that is that the total distance of the upward and downward propagating longitudinal waves in the liquid layer for 400 L and 600 L is less than that for the reaming cases (1000 L and 1800 L). 3.3. Estimating Liquid Height The arrival times of the reflected waves from the liquid are listed in Table 4 for clarity. By substituting these times into Equations (3) and (6), the total traveled distance in the liquid (S + S ) and h are obtained for all cases. The actual liquid height is obtained from the relationship 1 2 between the liquid volume and the cross-sectional area of the liquid, which is 200 mm . The purpose of this section is to validate the feasibility of the method by comparing the obtained height from Equation (6) with the actual height of the fluid measured. Additionally, the obtained speed of sound for water is compared with its theoretical value. Table 4. Velocity and height measurement. Actual Height t t t C Error in C S + S h Error in h A B c LW LW 1 2 (mm) (s) (s) (s) (m/s) (%) (mm) (mm) (%) 400 L 2 80.96 84.19 87.18 1427.5 3.54% 4.8 2.07 3.7 600 L 3 80.96 85.51 87.18 1520.1 2.71% 6.7 2.92 2.6 1000 L 5 80.96 88.64 87.21 1501 1.42% 11.4 4.93 1.4 1800 L 9 80.96 96.36 87.22 1347.4 8.96% 22.8 9.89 9.8/2.7 * * Represents the calibrated error in hours for the case of 1800 L as explained in Section 3.3. The percentage errors in the liquid height for 400 L, 600 L, 1000 L, and 1800 L are 3.7%, 2.6%, 1.4%, and 9.8%, respectively. As expected, in the case of 1800 L, the error is high because the height is above 0.86 L, so the obtained (S + S ) is not accurate. This case represents the second 1 2 case that is explained in Appendix A.2. To address this issue, the total traveled distance was found via parametric CAD software (Inventor Autodesk 201), as illustrated in Figure 7, for the critical case, 1000 L, and 1800 L. From this figure, one can observe that the total traveled distance (S + S ) 1 2 for 1000 L exactly matches the value found in Table 4. By contrast, for 1800 L, the total traveled distance does not exactly match the table. The corrected value for the case of 1800 L from the figure is 21.31 mm, which gives a C of 1383 m/s and height of 9.24 mm. Therefore, the error for 1800 L is LW dramatically reduced to 2.7%. The error in the height estimation might be caused by several factors, such as the theoretical value of the speed of sound in water and air, which mainly varies with the temperature, the surface tension phenomenon, and the estimated area of the liquid container. Acoustics 2020, 2, 366–381  376 of 381  Critical 1000µL 1800µL Acoustics 2020, 2 376 Acoustics 2020, 2, 366–381  376 of 381  Critical 1000µL 1800µL     (a)  (b)  (c)  Figure 7. The CAD results for the wave traveling in the liquid, showing the actual total traveled  distance for three cases: the (a) critical case; (b) 1000 μL case, and (c) 1800 μL case.      The error in the height estimation might be caused by several factors, such as the theoretical  value of the speed of sound in water and air, which mainly varies with the temperature, the surface  (a)  (b)  (c)  tension phenomenon, and the estimated area of the liquid container.  Figure 7. The CAD results for the wave traveling in the liquid, showing the actual total traveled Figure 7. The CAD results for the wave traveling in the liquid, showing the actual total traveled  distance for three cases: the (a) critical case; (b) 1000 L case, and (c) 1800 L case. distance for three cases: the (a) critical case; (b) 1000 μL case, and (c) 1800 μL case.  3.4. Short‐Time Fourier Transform Analysis for Both the Reflected Wave from the Defect (Edge) and the  Liquid  3.4. Short-Time Fourier Transform Analysis for Both the Reflected Wave from the Defect (Edge) and the Liquid The error in the height estimation might be caused by several factors, such as the theoretical  The goal of Short‐Time Fourier Transform Analysis (STFT) is to determine the effect of fluid  value of the speed of sound in water and air, which mainly varies with the temperature, the surface  The goal of Short-Time Fourier Transform Analysis (STFT) is to determine the e ect of fluid existence and fluid volume on the signal frequency. STFT is a useful technique to convert the time  existence tension phen andomenon, fluid volume  and the on esti thema signal ted are frequency a of the .liSTFT quid cont is a ainer. useful  technique to convert the time domain response of the signal into the frequency‐time domain for a selected window. The resolutions  domain response of the signal into the frequency-time domain for a selected window. The resolutions of  time  and frequency are  inversely  proportional;  as  the  frequency  resolution  increases,  the  time  3.4. Short‐Time Fourier Transform Analysis for Both the Reflected Wave from the Defect (Edge) and the  of time and frequency are inversely proportional; as the frequency resolution increases, the time resolution  decreases,  and  vice  versa  [32].  The  longer  the  window  is,  the  higher  the  frequency  Liquid  resolution decreases, and vice versa [32]. The longer the window is, the higher the frequency resolution resolution that will be obtained with a lower time resolution [33]. For this reason, a trade‐off between  that will be obtained with a lower time resolution [33]. For this reason, a trade-o between frequency The goal of Short‐Time Fourier Transform Analysis (STFT) is to determine the effect of fluid  frequency resolution and time resolution should be carefully implemented depending on which is  resolution and time resolution should be carefully implemented depending on which is more important existence and fluid volume on the signal frequency. STFT is a useful technique to convert the time  more important for a particular study. In this study, we utilized MATLAB (signal processing) to  for a particular study. In this study, we utilized MATLAB (signal processing) to obtain the STFT domain response of the signal into the frequency‐time domain for a selected window. The resolutions  obtain the STFT for the RWE (Reflected Wave from the Edge) and RWL (Reflected Wave from the  for the RWE (Reflected Wave from the Edge) and RWL (Reflected Wave from the Liquid) windows. of  time  and frequency are  inversely  proportional;  as  the  frequency  resolution  increases,  the  time  Liquid) windows. The time resolution was set to be 1 μs. The settings for the leakage and overlap are  The time resolution was set to be 1 s. The settings for the leakage and overlap are 1% and 99%, resolution  decreases,  and  vice  versa  [32].  The  longer  the  window  is,  the  higher  the  frequency  1%  and  99%,  respectively.  Figure  8  represents  the  STFT  of  the  RWE  and  RWL  for  all  cases.  For  respectively. Figure 8 represents the STFT of the RWE and RWL for all cases. For instance, Figure 8a1,b1 resolution that will be obtained with a lower time resolution [33]. For this reason, a trade‐off between  instance, Figure 8a1,b1 show the STFT results for the empty case obtained for the RWE and RWL,  show the STFT results for the empty case obtained for the RWE and RWL, respectively. Figure 8a2,b2 frequency resolution and time resolution should be carefully implemented depending on which is  respectively.  Figure  8a2,b2  show  the  STFT  for  400 μL  cases  obtained  for  the  RWE  and  RWL,  show the STFT for 400 L cases obtained for the RWE and RWL, respectively, and so on. The x-axis more important for a particular study. In this study, we utilized MATLAB (signal processing) to  respectively, and so on. The x‐axis represents the time in μs, and the y‐axis represents the frequency  represents the time in s, and the y-axis represents the frequency in MHz. The light-yellow(-dB), obtain the STFT for the RWE (Reflected Wave from the Edge) and RWL (Reflected Wave from the  in MHz. The light‐yellow(‐dB), which is close to 0 dB, represents the dominant frequency components  which is close to 0 dB, represents the dominant frequency components of the signal at a specific time. Liquid) windows. The time resolution was set to be 1 μs. The settings for the leakage and overlap are  of the signal at a specific time. If the yellow color becomes darker or changes to blue in a particular  If the yellow color becomes darker or changes to blue in a particular region, it indicates that a lower 1%  and  99%,  respectively.  Figure  8  represents  the  STFT  of  the  RWE  and  RWL  for  all  cases.  For  region, it indicates that a lower frequency component of the signal is localized.  frequency component of the signal is localized. instance, Figure 8a1,b1 show the STFT results for the empty case obtained for the RWE and RWL,  respectively.  Figure  8a2,b2  show  the  STFT  for  400 μL  cases  obtained  for  the  RWE  and  RWL,  respectively, and so on. The x‐axis represents the time in μs, and the y‐axis represents the frequency  in MHz. The light‐yellow(‐dB), which is close to 0 dB, represents the dominant frequency components  of the signal at a specific time. If the yellow color becomes darker or changes to blue in a particular  region, it indicates that a lower frequency component of the signal is localized.  (a1)  (b1)  Figure 8. Cont. (a1)  (b1)  Acoustics 2020, 2 377 Acoustics 2020, 2, 366–381  377 of 381  Fi t L k R l i h W SdL k R lihW (b2)  (a2)  (a3)  (b3)  (a4)  (b4)  (a5)  (b5)  Figure Figure8. 8. ((aa)) Short-T Short‐Time ime Fourier Fourier TTransform ransform for  forthe  ther reflection eflection fr from om edge  edge/co /corner rnerin inall  allcases:  cases: ((a1 a1)) empty empty, ,  (a2 (a2 ))400  400 μ L,L, ( a3 (a3 ) ) 600  600 μ L,L, (a4 (a4 ) 100 ) 1000 0  μ L,L, and  and (a5 (a5 ) 1800 ) 1800 L; μL; (b )(b STFT ) STFT for for the the reflection  reflection from from the the liquid  liqu inid all in  cases: (b1) empty, (b2) 400 L, (b3) 600 L, (b4) 1000 L, and (b5) 1800 L. all cases: (b1) empty, (b2) 400 μL, (b3) 600 μL, (b4) 1000 μL, and (b5) 1800 μL.  Acoustics 2020, 2 378 From Figure 8a1–a5, it can be observed that the central frequency of the RWE for all cases is lower than in the case of the empty container. A slight change in the fundamental frequency as the volume of liquid increases can be seen. Besides, multiple reflections from liquid appear before and after the RWE as the volume of liquid increases. From Figure 8b1–b5, it can be observed the first leaky Rayleigh wave, at the first edge/corner of the container, with a frequency of 3.5 to 4 MHz, occurs at a time between 80 s and 82 s for all cases except the empty container. The second leaky Rayleigh wave, at the end edge/corner of the container, appears at a time between 86 s and 88 s. The first leaky Rayleigh wave and the second leaky Rayleigh wave are denoted with solid red arrows and dashed red arrows, respectively, in Figure 8b2. Additionally, multiple reflections from the top surface of the liquid appear as the light-yellow color between or after the two Leaky Rayleigh waves based on the liquid volume, as previously explained in Section 3.2. Note that the first and second Leaky Rayleigh waves occurred at the same time plots (Figure 8b2–b5). 4. Conclusions In this paper, the impact of liquid presence on a solid surface on surface acoustic waves (SAWs) was experimentally investigated. Additionally, with the aid of the fact that when a SAW interacts with a liquid as it is traveling along the solid surface, some of its energy is transmitted through the liquid and some energy is reflected, the liquid height can be accurately estimated via analyzing the time domain response of the received signal. The results show that the peak-to-peak amplitude of the received SAW signal is dramatically reduced when liquid is present on the solid surface by almost 62.5% compared to the free surface (no liquid). With an increase in liquid volume, the peak-to-peak amplitude is slightly decreased, which indicates that the SAW is more sensitive to the area being covered by a liquid than the volume of the liquid. The results further show the capability of utilizing SAW to precisely measure the liquid height, with a small error that does not exceed 10% in all the tested cases in this study. Author Contributions: Conceptualization, H.A. and R.G.; methodology, H.A. and R.G.; software, H.A.; validation, H.A.; formal analysis, H.A.; investigation, H.A.; resources, R.G.; data curation, H.A. and R.G.; writing—original draft preparation, H.A.; writing—review and editing, R.G.; visualization, H.A.; supervision, R.G.; project administration, R.G.; funding acquisition, R.G. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest. Appendix A Appendix A.1 Finding the Refraction Angle To find the refraction angle at the solid–fluid interface ( ), Equation (A1) can be utilized. The theoretical value of C at a temperature of 20 C, C , and  are 1480 m/s, 2975.3 m/s, and 90 , Lw LR LR respectively. By substituting these values into Snell’s law, as illustrated in Equation (A1), we get: C sin( ) = C sin( ) (A1) LR 1 Lw R 2975.3 sin( ) = 1480 sin(90) (A2) = 29.83 (A3) The critical incident angle of the liquid can be obtained by substituting  = 90 , C , and C air Lw air into Snell’s law, as in Equation (A4): C sin( ) = C sin( ) (A4) air air LW critcal Acoustics 2020, 2 379 343 sin(90) = 1480 sin( ) (A5) critical = 13.40 (A6) critical Appendix A.2 The Derivation Equation for the Second Case when h > 0.86 L Equation (6) can no longer be applicable if the incident wave reflected from the liquid–air interface will hit the container edge at some height before it is reflected toward the solid surface with an incident angle of  , and it travels a distance of S . Therefore, the total distance traveled in the liquid is S + S + 3 3 1 2 S , as shown in Figure 2b. The angle  is measured by substituting the longitudinal velocity of the PLA 3 3 container, which is experimentally determined to be between 2200 m/s and 2300 m/s, depending on various conditions [31], the velocity of the liquid, and angle  into Snell’s law. The obtained angle 2 3 is 50.7 when using the velocity of 2300 m/s. The error in the height measurement will be high if Equation (6) is utilized, since the S value is neglected. Hence, a modification of Equation (6) should be implemented to improve the accuracy of the height measurement. Through analyzing the vector (S , S , S ) components with trigonometry as 1 2 3 illustrated in Figure 2b, the imaginary part (y) and the real part (x) are derived in terms of  ,  , and L 1 3 as: y : S cos  S cos  S sin  = 0 (A7) 1 1 2 1 3 3 x : S sin  + S sin  S cos  = L S cos  (A8) 2 3 3 3 3 1 1 1 By substituting S = h/cos into the previous equations and solving for S and S in terms of h,  , 1 1 2 3 1 , and L, we obtain: h sin y : S = S (A9) 2 3 cos  cos 1 1 L h x : S = (A10) sin  cos 1 1 Solving the two equations, S can be found as: 2h (L  cot  ) S = (A11) sin If h = 10 mm, L = 8 mm,  = 29.83 , and  = 50.7 and substituting these values into 1 3 Equations (5), (A10), and (A11), we get S , S , and S equal to 11.52 mm, 4.55 mm, and 7.816 mm, 1 2 3 respectively. It can be observed that S < S + S , which verifies the fact that Equation (6) cannot be 1 2 3 applicable when h > 0.86 L. Note that Equation (A11) shows that the height (h) in this case is a function of S , whereas it is a function of S in Equation (A9). 3 2 References 1. Chamuel, J.R. Laboratory studies on pulsed leaky Rayleigh wave components in a water layer over a solid bottom. In Shear Waves in Marine Sediments; Springer: Berlin/Heidelberg, Germany, 1991; pp. 59–66. 2. Cheeke, J.D.N. Fundamentals and Applications of Ultrasonic Waves; CRC Press: Boca Raton, FL, USA, 2016. 3. Überall, H. Surface waves in acoustics. Phys. Acoust. 1973, 10, 1–60. 4. Stoneley, R. Elastic waves at the surface of separation of two solids. In Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character; Royal Society: London, UK, 1924; Volume 106, pp. 416–428. 5. Thompson, D.O.; Chimenti, D.E. Review of Progress in Quantitative Nondestructive Evaluation; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2012; Volume 18. 6. Zhu, J.; Popovics, J.S.; Schubert, F. 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Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acoustics Multidisciplinary Digital Publishing Institute

Contactless Liquid Height and Property Estimation Using Surface Acoustic Waves

Acoustics , Volume 2 (2) – Jun 6, 2020

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acoustics Article Contactless Liquid Height and Property Estimation Using Surface Acoustic Waves 1 , 2 2 , Hani Alhazmi and Rasim Guldiken * Mechanical Engineering Department, Umm Al-Qura University, Makkah 21955, Saudi Arabia; haalhazmi@mail.usf.edu Mechanical Engineering Department, University of South Florida, Tampa, FL 33620, USA * Correspondence: guldiken@usf.edu; Tel.: +1-813-974-5628 Received: 24 April 2020; Accepted: 4 June 2020; Published: 6 June 2020 Abstract: The propagation of surface acoustic waves over a solid plate is highly influenced by the presence of liquid media on the surface. At the solid–liquid interface, a leaky Rayleigh wave radiates energy into the liquid, causing a signification attenuation of the surface acoustic wave amplitude. In this study, we take advantage of this spurious wave mode to predict the characteristics of the media, including the volume or height. In this study, the surface acoustic waves were generated on a thick 1018 steel surface via a 5 MHz transducer coupled through an angle beam wedge. A 3D-printed container was inserted on the propagation path. The pulse-echo time-domain responses of the signal were recorded at five di erent volumes (0, 400, 600, 1000, and 1800 L). With the aid of parametric CAD analysis, both the position and distance of the entire traveling wave in the liquid layer were modeled and verified with experimental studies. The results indicated that the average drop in the reflected wave amplitude due to liquid loading is 62.5% compared to the empty container, with a percentage of error within 10% for all cases. The localized-time frequency components of the reflected wave were obtained via a Short-Time Fourier Transform technique. Up to 10% reduction (500 KHz) in the central frequency was observed due to the liquid volume increasing. The method discussed herein could be useful for many applications, where some of the liquid’s parameters or the ultrasonic wave behavior in the liquid need to be assessed. Keywords: surface acoustic wave; attenuation; leaky Rayleigh wave; Short-Time Fourier Transform Analysis 1. Introduction Surface acoustic waves (SAWs) have been widely utilized to detect surface defects in many structural health monitoring applications. The propagation of SAWs over a thick solid plate is highly influenced by the presence of liquid on the surface. Therefore, the estimation of the defect location or depth can be inaccurate since the output signal includes additional wave packets, which is caused by the presence of liquid on the surface. In this study, we take advantage of these spurious wave packets to understand the characteristics of the liquid media. At the solid–liquid interface, a leaky Rayleigh wave is actuated, which radiates energy into the liquid, causing a signification drop in the SAW amplitude [1–3]. Due to the di erence in the acoustic impedance between the solid and liquid at the interface, a refracted longitudinal wave propagates into the liquid layer until it hits the liquid–air boundary and returns to the solid surface. The theory of elastic wave propagation along an interface between two media has been well studied. For instance, Stonely solved the wave propagation along a solid–solid interface (Stoneley’s waves) [4], whereas Scholte studied the wave propagation along a solid–liquid interface (Scholte’s waves) [5,6]. The Rayleigh wave and leaky Rayleigh wave at the solid–liquid interface were studied [6]. Acoustics 2020, 2, 366–381; doi:10.3390/acoustics2020021 www.mdpi.com/journal/acoustics Acoustics 2020, 2 367 The leaky Rayleigh wave exists at the interface when the longitudinal velocity of the liquid is smaller than the shear wave velocity in the solid half-space [7,8]. The propagation of surface waves along the solid–liquid interface, where the liquid velocity is higher than the shear velocity in the solid, was investigated theoretically and experimentally by Padilla for the existence of a surface wave at a plastic–liquid interface [9]. The multiple pulsed leaky Rayleigh wave component propagation in the liquid layer over an aluminum plate was experimentally studied, and the velocity of the pulsed leaky Rayleigh wave was found to be higher than the Rayleigh wave velocity, while the amplitude of the pulsed leak Rayleigh components was increased [1]. SAW (or Rayleigh wave)-based devices, which are typically made of anisotropic materials such as LiNbO , where the SAW characteristics depend on the orientation, have gained considerable attention [10]. The sensitivity of SAWs to liquid-loading on the SAW devices has led to a wide range of applications such as liquid shear viscosity measurement [11], glycerin concentration sensing in a microfluidic channel [12], early ovarian cancer detection [13,14], particle and cell separation [15–17], and liquid mixing and pumping in microchannels [18,19]. Other useful applications of SAWs are quantifying cell growth [20], quantifying bolt tension in bolted joints [21,22], and pH sensing in cultures [23]. By contrast, only a few applications have taken advantage of the e ect of liquid-loading over a solid material (isotropic) on SAWs. One possible application would be estimating liquid height using SAWs. In literature, there are a couple of methods for determining liquid height via using a single or multiple ultrasonic transducer(s), where the basic principle works on the discrepancy in the acoustic impedance of the two media. In one of the studies, the liquid height was measured utilizing two ultrasonic transducers coupled to a tank wall. The first transducer transmits the bulk shear wave that propagates along the solid member in a zigzag path, and the second transducer receives the reflected wave from the solid–liquid interface. Based on the attenuated amplitude of the signal, the acoustic impedance of the liquid can be measured [24]. A non-contact ultrasonic PING sensor was utilized to measure water height with the aid of a microcontroller to calculate the change in the arrival times of the echoes from water [25]. Another method measured liquid height by utilizing three transducers; one transmitter was located between the two echo receiving transducers, and these transducers were encapsulated to overcome the coupling issue. The measurement was achieved by moving the transducers along the container wall, and a noticeable di erence in the reflected wave energy was observed when the transmitter moved from the above liquid level to the below liquid level [26]. The advantages of employing SAWs in detecting surface flaws are that they propagate close to the free surface of a specimen, are easy to excite and record, and are less complicated compared to other types of ultrasonic waves [27–29]. The proposed method to measure fluid height via SAWs is simple, fast, and inexpensive. Moreover, the proposed methodology has the capability to measure a small amount of fluid on a solid surface, such as a spill from a distance, with a small error. The measurement can be achieved by exciting the SAW through an o -shelf piezoelectric transducer connected to the angle beam wedge. The wave reflected from the liquid propagates back towards the transducer, and the received signal is recorded via an oscilloscope. Performing a thorough analysis of the time domain response of the received signal determines the arrival time of the leaky Rayleigh wave from the solid–fluid interface and the arrival time of the reflected wave from the top surface of the fluid. In the final step, a height equation that is derived from Snell’s law and the fluid proprieties can be utilized to accurately find the height. There are two primary aims of this study. The first goal is to investigate the e ect of liquid loading on the propagating SAWs over a solid surface and how the reflected wave from a defect changes due to the existence of liquid media in the propagation path. The second aim is to investigate the capability of measuring the liquid level that is present on the specimen’s surface via SAWs. Understanding how a liquid influences the SAW signal is essential when the SAWs are utilized in a structural health-monitoring application. It is also vital to estimate the liquid properties if the height and surface parameters are known. Acoustics 2020, 2 368 Acoustics 2020, 2, 366–381  368 of 381  2. Methodology 2. Methodology  2.1. Operation Principle 2.1. Operation Principle  When the surface acoustic wave (SAW) arrives at the first point of contact between the liquid When the surface acoustic wave (SAW) arrives at the first point of contact between the liquid  and solid surface, some energy radiates into liquid due to the di erence in the acoustic impedance and solid surface, some energy radiates into liquid due to the difference in the acoustic impedance  between the two media. The acoustic impedance strongly depends on the density and velocity of between the two media. The acoustic impedance strongly depends on the density and velocity of the  the medium, where the density is much higher in solids than in liquids. medium, where the density is much higher in solids than in liquids.  Z = c (1) 𝑍 𝑐𝜌   (1) 2 2 3 3 where Z is the acoustic impedance (rayl/m ),  is the density of medium (kg/m ), and c is the sound  where Z is the acoustic impedance (rayl/m ),  is the density of medium (kg/m ), and c is the sound speed through the material (m/s). The reflection coefficient can be expressed in Equation (2):  speed through the material (m/s). The reflection coecient can be expressed in Equation (2): 𝜌 𝐶 𝜌 𝐶 C  C 𝑅   2 2 1 1 (2) R = (2) 𝜌 𝐶 𝜌 𝐶 C +  C 1 1 2 2 Along the liquid–solid interface, the wave propagates as a leaky Rayleigh wave (LRW) with a  Along the liquid–solid interface, the wave propagates as a leaky Rayleigh wave (LRW) with higher  velocity  compared  to  the  SAW  (Rayleigh  wave),  and  its  amplitude  decays,  since  energy  a higher velocity compared to the SAW (Rayleigh wave), and its amplitude decays, since energy continues radiating into the liquid [1–3]. Due to the difference in the speed of sound between the  continues radiating into the liquid [1–3]. Due to the di erence in the speed of sound between the liquid liquid and leaky Rayleigh wave, the wave at the interface is refracted from the solid to the liquid at  and leaky Rayleigh wave, the wave at the interface is refracted from the solid to the liquid at angle angle θ1 with respect to the normal axis. Besides, the shear wave cannot be supported in the liquid  with respect to the normal axis. Besides, the shear wave cannot be supported in the liquid layer [29]. layer [29].  The leaky Rayleigh wave velocity, which depends on the types of the two materials at the interface, The  leaky  Rayleigh  wave  velocity,  which  depends  on  the  types  of  the  two  materials  at  the  can be found through experimentation. For example, the speed of sound was experimentally measured interface,  can  be  found  through  experimentation.  For  example,  the  speed  of  sound  was  for the air–aluminum interface as 2964 m/s, whereas the SAW for aluminum is 2952 m/s [1]. In this study, experimentally  measured  for  the  air–aluminum  interface  as  2964  m/s,  whereas  the  SAW  for  we experimentally obtained the leaky Rayleigh wave velocity, which is presented in the experiment aluminum is 2952 m/s [1]. In this study, we experimentally obtained the leaky Rayleigh wave velocity,  results section. which is presented in the experiment results section.  The refraction angle  can be estimated by substituting the longitudinal wave velocity of The  refraction  angle θ1  can  be  estimated  by  substituting  the  longitudinal  wave  velocity  of  deionized water (C ), the leaky Rayleigh wave velocity (C ), and the propagation angle of the SAW Lw LR deionized water (CLw), the leaky Rayleigh wave velocity (CLR), and the propagation angle of the SAW  ( ) into Snell’s law (see Appendix A). (θR) into Snell’s law (see Appendix A).  Once the refracted wave in the liquid reaches the liquid–air boundary, it is reflected with angle Once the refracted wave in the liquid reaches the liquid–air boundary, it is reflected with angle  with respect to the normal axis at the interface due to the large di erence in the speed of sound θ2 with respect to the normal axis at the interface due to the large difference in the speed of sound for  for the two media. Hence, no refraction occurs into the air, and Snell’s law can no longer be satisfied. the two media. Hence, no refraction occurs into the air, and Snell’s law can no longer be satisfied. The  The critical incident angle of liquid can be obtained by substituting  = 90 and C and C into air Lw air critical incident angle of liquid can be obtained by substituting θair = 90° and CLw and Cair into Snell’s  Snell’s law (see Appendix A). law (see Appendix A).  If the incident angle from the liquid is higher than the critical angle, the wave will be reflected If the incident angle from the liquid is higher than the critical angle, the wave will be reflected  entirely at the liquid–air interface, as illustrated in Figure 1a. If the incident angle from the liquid is entirely at the liquid–air interface, as illustrated in Figure 1a. If the incident angle from the liquid is  equal to the critical angle, the refracted wave travels parallel to the interface between the air and liquid, equal to the critical angle, the refracted wave travels parallel to the interface between the air and  as shown in Figure 1b. In this study, as the  >> c , the wave will be reflected with angle  , 1 ritical 2 liquid, as shown in Figure 1b. In this study, as the θ1 >> critical, the wave will be reflected with angle  which is equal to  , as illustrated in Figure 1a. θ2, which is equal to θ1, as illustrated in Figure 1a.  (a)  (b)  Figure 1. (a) Schematic representation of a wave traveling in the liquid when the reflected angle at the solid–liquid Figure 1. (a) Schematic representation of a wave traveling in the liquid when the reflected angle at the  solid–liquid interface is larger than the critical angle; (b) Schematic representation of a wave traveling  in the liquid when the reflected angle at the solid–liquid interface is equal to the critical reflected  angle.  Acoustics 2020, 2 369 Acoustics 2020, 2, 366–381  369 of 381  interface is larger than the critical angle; (b) Schematic representation of a wave traveling in the liquid when the reflected angle at the solid–liquid interface is equal to the critical reflected angle. 2.2. Liquid Height Estimation  2.2. Liquid Height Estimation The liquid height can be estimated by using the arrival time of the leaky Rayleigh wave (tA),  The liquid height can be estimated by using the arrival time of the leaky Rayleigh wave (t ), which occurs at the solid–fluid interface, and the arrival time of the reflected wave from the top A   which occurs at the solid–fluid interface, and the arrival time of the reflected wave from the top surface surface of the fluid (tB). Besides these values, the theoretical speed of sound for the fluid and the  of the fluid (t ). Besides these values, the theoretical speed of sound for the fluid and the refraction refraction angle B  at the interface (θ1) are used in determining the liquid height.  angle at the interface ( ) are used in determining the liquid height. Since the liquid is held 1  in a finite container, two cases are expected to exist, as shown in Figure  Since the liquid is held in a finite container, two cases are expected to exist, as shown in Figure 2. 2. The first case occurs when the propagating wave in the liquid hits the liquid–air boundary and  The first case occurs when the propagating wave in the liquid hits the liquid–air boundary and reflects reflects directly to the solid–liquid interface. By contrast, in the second case, the reflected wave hits  directly to the solid–liquid interface. By contrast, in the second case, the reflected wave hits the container the container edge before reaching the solid–liquid interface. These two cases rely mainly on the ratio  edge before reaching the solid–liquid interface. These two cases rely mainly on the ratio of the liquid of the liquid height to the particular container dimensions. Based on the calculation of incident angle  height to the particular container dimensions. Based on the calculation of incident angle  ,  , θ1,  θ3,  and  the  geometric  dimensions  of  the  container,  the  first  case  occurs  if  the  height 1   is 3  and the geometric dimensions of the container, the first case occurs if the height is approximately in approximately in the range of (0 < h < 0.86 L). By contrast, the second case occurs if the height is higher  the range of (0 < h < 0.86 L). By contrast, the second case occurs if the height is higher than 0.86 L. than 0.86 L.      (a)  (b)  Figure Figure 2. 2. (a (a) )Sche Schematic matic representation representation ofof a wa a wave ve traveling traveling  at a at different a di erent  leve level l of li of qui liquid, d, inclu including ding the  critica the critical l case case, , whiwhich ch occurs occurs  at hat < h0.< 860.86  L (first L (first  case case); ); (b) Schem (b) Schematic atic representation representation  of a of wave a wave  traveling traveling  in  the in the  liqu liquid id whe when n the the  liqu liquid id height height  is higher is higher  than than  0.86 0.86  L (c La(case se 2).2).   The total distance the propagating wave travels in the media is S + S as illustrated in Figure 2a. The total distance the propagating wave travels in the media is S 11 + S2, 2, as illustrated in Figure 2a.  S and S are the distances traveled by the incident wave from the solid–liquid interface (upward) S1 1 and S22 are the distances traveled by the incident wave from the solid–liquid interface (upward)  and liquid–air interface (downward), respectively, and L is the actual length of the container. Since and liquid–air interface (downward), respectively, and L is the actual length of the container. Since  the incident angle from the liquid ( ) and the reflected angle at the liquid-air interface ( ) are equal, the incident angle from the liquid (θ1 1) and the reflected angle at the liquid‐air interface (θ2 2) are equal,  S = S . For the experimental tests, the total distance traveled by a propagating wave in a medium can S1 1 = S2. 2 For the experimental tests, the total distance traveled by a propagating wave in a medium can  be expressed as: be expressed as:  S + S = C  (t t ) (3) 1 2 Lw B A 𝑆 𝑆 𝐶 𝑡 𝑡   (3) where t is the arrival time of the reflected wave from the liquid–air interface, and t is the arrival B A where tB is the arrival time of the reflected wave from the liquid–air interface, and tA is the arrival  time of a leaky Rayleigh wave at the solid–liquid interface. For accuracy purposes, both arrival times time of a leaky Rayleigh wave at the solid–liquid interface. For accuracy purposes, both arrival  should be chosen at the same phase. By substituting S = S into Equation (3), we get 1 2 times should be chosen at the same phase. By substituting S1 = S2 into Equation (3), we get  2S = C  (t t ) (4) 1 Lw B A 2𝑆 𝐶 𝑡 𝑡   (4) From the geometry, the liquid height can be determined as: From the geometry, the liquid height can be determined as:  S 𝑆 =   (5 (5)) cos cos𝜃( ) Substituting Equation (4) into Equation (5), we get:  (6) ℎ 𝑡 𝑡 cos𝜃   Acoustics 2020, 2 370 Substituting Equation (4) into Equation (5), we get: Lw h =  (t t )  cos( ) (6) Acoustics 2020, 2, 366–381  B A 1 370 of 381  As As can can be be observed observed frfrom om Equation Equation (6), (6), the the liquid liquid height height isisa afunction  functionof ofC CLw,, the the traveling traveling time time  Lw and the incident angle at the solid–liquid interface. The derivation of the equations for the second case and the incident angle at the solid–liquid interface. The derivation of the equations for the second  can casebe can found  be foin und Appendix  in Appendix A.  A.  2.3. Experimental Setup 2.3. Experimental Setup  The pulse-echo technique is utilized in this study, in which an ultrasonic wave is generated The pulse‐echo technique is utilized in this study, in which an ultrasonic wave is generated and  and received through using only one transducer. The generation of a SAW (Rayleigh wave) that received  through  using  only  one  transducer.  The  generation  of  a  SAW  (Rayleigh  wave)  that  propagates on the free surface of a solid specimen requires using a normal beam transducer, a comb propagates on the free surface of a solid specimen requires using a normal beam transducer, a comb  transducer, or a transducer that is attached to an angle beam wedge placed on the specimen’s surface. transducer, or a transducer that is attached to an angle beam wedge placed on the specimen’s surface.  The purpose of the angle beam wedge is to convert the longitudinal wave generated via the ultrasonic The purpose of the angle beam wedge is to convert the longitudinal wave generated via the ultrasonic  transducer into a Rayleigh wave at the interface between the wedge surface and the specimen’s transducer  into  a  Rayleigh  wave  at  the  interface  between  the  wedge  surface  and  the  specimen’s  surface [30]. Snell’s law should be considered to calculate the appropriate incident angle inside surface [30]. Snell’s law should be considered to calculate the appropriate incident angle inside the  the wedge to achieve the desired angle of SAW propagation (90 ). As illustrated in Figure 3, the angle wedge to achieve the desired angle of SAW propagation (90°). As illustrated in Figure 3, the angle  beam wedge (ABWML-5T 90, Olympus NDT, Waltham, MA, USA) used in this experiment is made of beam wedge (ABWML‐5T 90, Olympus NDT, Waltham, MA) used in this experiment is made of  plastic (Lucite), with a longitudinal wave velocity of 2700 m/s. By substituting the longitudinal velocity plastic  (Lucite),  with  a  longitudinal  wave  velocity  of  2700  m/s.  By  substituting  the  longitudinal  of the wedge and the theoretical Rayleigh wave velocity for a 1018 steel (2953 m/s) into Snell’s law, velocity of the wedge and the theoretical Rayleigh wave velocity for a 1018 steel (2953 m/s) into Snell’s  the incident angle inside the wedge is found to be 66.12 . law, the incident angle inside the wedge is found to be 66.12°.  (a)  (b)  Figure Figure 3. 3. ((aa)) Sc Schematic hematic diagram diagram for for the the expe experiment riment setu setup; p; (b)( bThe ) The  contain container er dimensions dimensions  used u sed in this in  this studstudy y.  . The ultrasonic pulser/receiver (5072PR, Olympus NDT, Waltham, MA, USA) is utilized to excite The ultrasonic pulser/receiver (5072PR, Olympus NDT, Waltham, MA, USA) is utilized to excite  a pulse to a 5 MHz transducer (C541-SM, Olympus NDT, Waltham, MA, USA), which is attached to a pulse to a 5 MHz transducer (C541‐SM, Olympus NDT, Waltham, MA, USA), which is attached to  the angle beam wedge. The received signal can then be amplified before it is transferred to a digital the angle beam wedge. The received signal can then be amplified before it is transferred to a digital  oscilloscope. The amplifier is built in the pulser/receiver, which can be used to control either the gain oscilloscope. The amplifier is built in the pulser/receiver, which can be used to control either the gain  (+dB) or the attenuation (dB) of the received signal. The pulser/receiver has a low pass filter at 10 MHz (+dB) or the attenuation (−dB) of the received signal. The pulser/receiver has a low pass filter at 10  and a high pass filter at 1 MHz. The signal is recorded with 128 averaging to increase the signal-to-noise MHz and a high pass filter at 1 MHz. The signal is recorded with 128 averaging to increase the signal‐ ratio with a digital Oscilloscope (TDS2001C, Tektronix, Beaverton, OH, USA). The sampling time to‐noise ratio with a digital Oscilloscope (TDS2001C, Tektronix, Beaverton, OH, USA). The sampling  time rate was kept constant at 25 μs for the 5 MHz transducer in all recorded signals to avoid aliasing.  The pulser/receiver settings are listed in Table 1.  Acoustics 2020, 2 371 rate was kept constant at 25 s for the 5 MHz transducer in all recorded signals to avoid aliasing. The pulser/receiver settings are listed in Table 1. Table 1. The pulser/receiver settings used during the experimental studies. High Pass Low Pass PRF(Hz) Energy Damping (50 W) Amplifier (Gain) Filter (HPF) Filter (LPF) 100 1 3 1 MHz 10 MHz 30 db The containers were filled with a precise amount of deionized (DI) water via an Eppendorf Research Pipette that can hold 0 to 100 L of liquid. The pipette’s accuracy was verified by dropping 100 L of DI water onto a sensitive scale (Scaout Pro SP402, Ohaus Inc., Parsippany, NJ, USA), and the obtained reading on the scale was used for calibration. The 3D-printed containers, which fit on the specimen’s surface, are made of Polylactic Acid material (PLA). The geometric dimensions of the container are 10 mm  22 mm  8 mm. To measure the actual covered area by the liquid, the container is fully occupied with liquid (2000 mm ) and then the volume is divided by the height of the container (10 mm), which gives the area as 200 mm . The primary purpose of using the container is to maintain the consistency of the area covered by liquid while recording the signal. Initial sets of experiments were conducted to verify that placing the container on the free surface of the specimen had no impact on the propagation of the SAWs. The experiment results confirm that there is no reflection from the containers, since the interface between the specimen’s surface and the container has no real area of contact. The distance between the container and transducer was selected to be 77 mm, which ensured that the container was placed beyond the near field distance (N), which can be estimated using Equation (7). D f N = (7) 4C where D is the transducer diameter, f is the signal frequency, and C is material sound speed. Substituting D = 12.7 mm (0.5 in), f = 5 MHz, and C = 2953 m/s (Rayleigh wave speed) into equation, the near field distance (N) will be 68.27 mm. The material properties for DI water, air, the PLA material, and 1081 steel are listed in Table 2. Table 2. The material properties for deionized (DI) water, air, the PLA material, and 1081 steel. Deionized Water 1018 Steel Air PLA (25 C) Density,  (g/cm ) 1 7.870 0.001 1.24 Speed of Sound (m/s) 1480 2953 (C.R.) 330–343 2200~2300 [31] The experimental procedure is as follows. First, the angle beam wedge is placed on the specimen surface after applying an ultrasonic couplant between the two surfaces to facilitate the ultrasonic wave transmission and reception from the wedge on the specimen surface and vice versa. A three-way C-clamp is used to ensure the wedge remains stationary throughout the experiment and to provide adequate contact between the specimen surface and wedge. Next, the container is placed on the free surface of the specimen (1018 Steel) 77 mm from the wedge tip, whereas the edge is 105 mm from the angle beam wedge. The container area in contact with the specimen is wrapped with a thread sealing tape to prevent the medium from leaking. The reflected signal from the edge for the empty container is selected as the reference for the experimental studies. Thirty seconds after filling the container with DI water, the received signal reflected from the edge of the specimen and the liquid are recorded separately to assist in the data analysis process. The data collection step is repeated for all the di erent liquid volumes investigated. The entire signal for the empty container is shown in Figure 4. It can be observed from this figure that reflection from the wedge-specimen interface is present at 29.2 s in the data, and the reflection from Acoustics 2020, 2 372 Acoustics 2020, 2, 366–381  372 of 381  the specimen edge is at time 99 s. Based on the experimental observation after filling the container Acoustics 2020, 2, 366–381  372 of 381  signal shown on the Oscilloscope, one for the reflection from the specimen edge (RWE) and the other  with liquid, the reflection of the wave from the medium will take place right after 80 s. For better one comparison  for the reflection among al from l cases,  the we liqudecided id (RWL) to as have  show two n in separate  Figurewindows  4.  for the received signal shown signal shown on the Oscilloscope, one for the reflection from the specimen edge (RWE) and the other  on the Oscilloscope, one for the reflection from the specimen edge (RWE) and the other one for one for the reflection from the liquid (RWL) as shown in Figure 4.  the reflection from the liquid (RWL) as shown in Figure 4. Echo from the edge Echo at the  wedge(29.2µs) Echo from the edge Echo at the  wedge(29.2µs) 0 10 203040 5060 708090 100 110 120 ‐1 0 10 203040 5060 708090 100 110 120 ‐2 ‐1 RWF window RWE window ‐3 ‐2 Time(µs) RWF window RWE window ‐3 Time(µs) Figure 4. The entire signal received for the empty container, including the selected windows for the  Figure 4. The entire signal received for the empty container, including the selected windows for reflection from the liquid and the reflection from the edge.  the reflection from the liquid and the reflection from the edge. Figure 4. The entire signal received for the empty container, including the selected windows for the  reflection from the liquid and the reflection from the edge.  3. Results and Discussion  3. Results and Discussion 3. Results and Discussion  3.1. The Effect of the Presence of Liquid Media on the Propagation Path of the Reflected Wave from a Defect  3.1. The E ect of the Presence of Liquid Media on the Propagation Path of the Reflected Wave from (Ed a g Defect e)  (Edge) 3.1. The Effect of the Presence of Liquid Media on the Propagation Path of the Reflected Wave from a Defect  It Itis isimper imperative ative toto stu study dy ho how w the the wa wave ve reflected reflected fro frm om the the ed edge ge is isininfluenced fluenced wh when en a sm a small all area area  (Edge)  ofof a tested a tested  specimen specimen  surfa surface ce is occ is occupied upied by li by quliquid id matter matter  in the in p the roppr agat opagation ion path,path,  mainly mainly  whenwhen  the  It is imperative to study how the wave reflected from the edge is influenced when a small area  medium the medium  is between is between  the transducer the transducer  and the and  defect the to defect  be detected. to be detected.  In generIn al,general,  the amplit theude amplitude  of SAWsof  of a tested specimen surface is occupied by liquid matter in the propagation path, mainly when the  sign SAif Ws icant significantly ly  attenuates attenuates   as  the  lias quthe id  in liquid teractinteracts s  with  thwith e  solid the  (s solid olid–(solid–liquid liquid  interact interaction) ion)  due  to due   theto  medium is between the transducer and the defect to be detected. In general, the amplitude of SAWs  diss theipat dissipation ion of theof signal the signal  energy ener  intgy o the into liqu theid. liquid.   significantly  attenuates  as  the  liquid  interacts  with  the  solid  (solid–liquid  interaction)  due  to  the  The The results results inindicate dicate tha that t the the pea peak-to-peak k‐to‐peak am amplitude plitude ofof the the reflected reflected wave wave from from the the edge edge dec declines lines  dissipation of the signal energy into the liquid.  sharp sharply ly when when 40400 0 μL Lofof DI DI water water is iad s added ded toto the the liq liquid uid container container and and slight slightly ly de decr creases eases oror rema remains ins  The results indicate that the peak‐to‐peak amplitude of the reflected wave from the edge declines  alm almost ost  const constant ant  as as the theliquid   liquid volume   volume incr   incr eases eases (Figur   (Fig eure 5). This   5).  Th indicates is  indithat cates the   tha change t  the  chan in thege amplitude   in  the  sharply when 400 μL of DI water is added to the liquid container and slightly decreases or remains  amplit is mor ude e sensitive  is more sens to the itiv areea tothan  the ar toea the tha liquid n to the volume  liquid pr volume esent in pthe resent propagation  in the prop path. agation path.  almost  constant  as  the  liquid  volume  increases  (Figure  5).  This  indicates  that  the  change  in  the  amplitude is more sensitive to the area than to the liquid volume present in the propagation path.  RWE Empty RWE Empty 94 95 96 97 98 99 100 101 102 103 104 ‐1 Time(µs) 94 95 96 97 98 99 100 101 102 103 104 ‐1 0.6 Time(µs) RWE 400µl 0.4 0.6 RWE 0.2 400µl 0.4 0.2 94 95 96 97 98 99 100 101 102 103 104 ‐0.2 ‐0.4 94 95 96 97 98 99 100 101 102 103 104 Time(µs) ‐0.2 ‐0.4 Figure 5. Cont. Time(µs) Amplitude(V) Amplitude(V) Amplitude(V) Amplitude(V) Amplitude(V) Amplitude(V) Acoustics 2020, 2 373 Acoustics 2020, 2, 366–381  373 of 381  0.6 600µl 0.4 0.2 94 95 96 97 98 99 100 101 102 103 104 ‐0.2 ‐0.4 Time(µs) 0.6 1000µl 0.4 0.2 94 95 96 97 98 99 100 101 102 103 104 ‐0.2 ‐0.4 Time(µs) 0.6 1800µl 0.4 0.2 94 95 96 97 98 99 100 101 102 103 104 ‐0.2 ‐0.4 Time(µs) Figure 5. Time domain response for the reflected wave from the edge for all cases. Figure 5. Time domain response for the reflected wave from the edge for all cases.  The average percentage of the peak-to-peak amplitude drop due to liquid exitance was 62.5%, The average percentage of the peak‐to‐peak amplitude drop due to liquid exitance was −62.5%,  as shown in Table 3. The maximum amplitude of the reflected wave from the edge remains constant as shown in Table 3. The maximum amplitude of the reflected wave from the edge remains constant  in all cases, which occurs at the time of 99.464 s (T ). It is important to note that the wave P-RWE in all cases, which occurs at the time of 99.464 μs (TP‐RWE). It is important to note that the wave reflected  reflected from the defect (edge or corner in this study) was not a ected by the presence of DI water on from the defect (edge or corner in this study) was not affected by the presence of DI water on the  the surface. By utilizing Equation (8)—where v is the theoretical velocity of the Rayleigh wave in surface. By utilizing Equation (8)—where vR is the theoretical velocity of the Rayleigh wave in 1018  1018 steel (2953 m/s) and T is the time associated with the maximum reflection at the angle beam p-wedge steel (2953 m/s) and Tp‐wedge is the time associated with the maximum reflection at the angle beam  wedge, which is 29.2 s—the obtained distance was 103.74 mm, where the actual distance between wedge, which is 29.2 μs—the obtained distance was 103.74 mm, where the actual distance between  the transducer and the edge was 105 mm. The reasonably low 1.9% error herein could be due to the transducer and the edge was 105 mm. The reasonably low 1.9% error herein could be due to the  the theoretical Rayleigh wave velocity or the measurement accuracy. theoretical Rayleigh wave velocity or the measurement accuracy.  T T  v (PRWE) (Pwedge) R Table 3. The percentage drop in the d  = peak‐to‐peak amplitude of the reflected wave from the edge for  (8) all cases.    Empty  400 μL  600 μL  1000 μL  1800 μL  Table 3. The percentage drop in the peak-to-peak amplitude of the reflected wave from the edge for P–P amplitude (V)  1.90  0.74  0.72  0.70  0.70  all cases. 𝑥 𝑒𝑡𝑚𝑝𝑦 % 100   ‐  −61.05 −62.11 −63.16 −63.16  𝑒𝑚𝑝𝑡𝑦 Empty 400 L 600 L 1000 L 1800 L P–P amplitude (V) 1.90 0.74 0.72 0.70 0.70 xempty % =  100 - 61.05 62.11 63.16 63.16 empty 𝑇 𝑇 𝑣 (8)  𝑑   The results further show that wave packets appear before and after the wave reflected from the edge, and they shift to the right as the volume of liquid increases, as shown in Figure 5. These The results further show that wave packets appear before and after the wave reflected from the  edge, and they shift to the right as the volume of liquid increases, as shown in Figure5. These waves  Amplitude(V) Amplitude(V) Amplitude(V) Acoustics 2020, 2 374 Acoustics 2020, 2, 366–381  374 of 381  are  multiple  reflections  from  the  top  surface  of  the  liquid.  The  shift  in  time  occurs  because  the  waves are multiple reflections from the top surface of the liquid. The shift in time occurs because reflected wave travels longer in liquid as the height of liquid increases.  the reflected wave travels longer in liquid as the height of liquid increases. 3.2. The Reflected Wave from the Liquid on the Propagation Path  3.2. The Reflected Wave from the Liquid on the Propagation Path Figure 6 shows the time‐domain responses of the wave reflected from the DI water for all the  Figure 6 shows the time-domain responses of the wave reflected from the DI water for all volumes investigated. Based on observations of the exact location of reflections from the liquid, a  the volumes investigated. Based on observations of the exact location of reflections from the liquid, window between the times of 74 and 98 μs was selected, which covers the region before the RWE. By  a window between the times of 74 and 98 s was selected, which covers the region before the RWE. choosing this window, not only can the first reflected wave from the liquid be easily detected, but the  By choosing this window, not only can the first reflected wave from the liquid be easily detected, behavior  of  the  reflected  signal  can  also  be  precisely  analyzed,  for  example,  the  peak‐to‐peak  but the behavior of the reflected signal can also be precisely analyzed, for example, the peak-to-peak amplitude of the reflected wave from the liquid. During the experiments, we carefully analyzed the  amplitude of the reflected wave from the liquid. During the experiments, we carefully analyzed obtained time‐domain signal of each case. In order to ensure the reflection of the signal was coming  the obtained time-domain signal of each case. In order to ensure the reflection of the signal was coming from the top surface of the fluid, we disturbed the top surface with a needle, and it was observed that  from the top surface of the fluid, we disturbed the top surface with a needle, and it was observed that the amplitude of the reflection died out. The dotted box (A), the dotted box (B), and the dotted box  the amplitude of the reflection died out. The dotted box (A), the dotted box (B), and the dotted box (C) (C) in Figure 6. represent the first leaky Rayleigh wave at the solid–liquid interface at the beginning  in Figure 6. represent the first leaky Rayleigh wave at the solid–liquid interface at the beginning of of the container, the first reflected wave from the top surface of the liquid, and the second leaky  the container, the first reflected wave from the top surface of the liquid, and the second leaky Rayleigh Rayleigh wave at the end of the container, respectively.  wave at the end of the container, respectively. Empty ‐50 74 76 78 80 82 84 86 88 90 92 94 96 98 Time(µs) ‐150 400µl C 74 76 78 80 82 84 86 88 90 92 94 96 98 ‐100 Time(µs) ‐200 600µl 74 76 78 80 82 84 86 88 90 92 94 96 98 ‐100 Time(µs) ‐200 1000µl 100 A ‐50 74 76 78 80 82 84 86 88 90 92 94 96 98 ‐100 Time(µs) ‐150 1800µl 100 B 74 76 78 80 82 84 86 88 90 92 94 96 98 ‐50 Time(µs) ‐100 Figure 6. Time domain responses for the reflected wave from the liquid for all cases. Figure 6. Time domain responses for the reflected wave from the liquid for all cases.  From the results of all the cases, it can be noted that the amplitude of the signal dramatically From the results of all the cases, it can be noted that the amplitude of the signal dramatically  changes when the container is filled with 400 L of liquid around the time of 80.96 s, as seen in changes when the container is filled with 400 μL of liquid around the time of 80.96 μs, as seen in  Figure 6. One can observe that the amplitude of the leaky Rayleigh wave is attenuated as it travels  Amplitude(mV) Amplitude(mV) Amplitude(mV) Amplitude(mV) Amplitude(mV) Acoustics 2020, 2 375 Figure 6. One can observe that the amplitude of the leaky Rayleigh wave is attenuated as it travels along the solid–liquid interface in all cases except one case (400 L). The velocity of the leaky Rayleigh wave at the beginning of the container can be obtained by utilizing Equation (8), where the maximum amplitude occurs at the time of 80.96 s, the actual distance between the transducer and container is 77 mm, and the time at the wedge is 29.2 s. Hence, the velocity obtained is 2975 m/s. The results further show that the first reflected wave from the top surface of the liquid arrives earlier than the first leaky Rayleigh wave in the cases of 400 L and 600 L, whereas it arrives later than the first leaky Rayleigh wave in the case of 1000 L and 1800 L. The reason for that is that the total distance of the upward and downward propagating longitudinal waves in the liquid layer for 400 L and 600 L is less than that for the reaming cases (1000 L and 1800 L). 3.3. Estimating Liquid Height The arrival times of the reflected waves from the liquid are listed in Table 4 for clarity. By substituting these times into Equations (3) and (6), the total traveled distance in the liquid (S + S ) and h are obtained for all cases. The actual liquid height is obtained from the relationship 1 2 between the liquid volume and the cross-sectional area of the liquid, which is 200 mm . The purpose of this section is to validate the feasibility of the method by comparing the obtained height from Equation (6) with the actual height of the fluid measured. Additionally, the obtained speed of sound for water is compared with its theoretical value. Table 4. Velocity and height measurement. Actual Height t t t C Error in C S + S h Error in h A B c LW LW 1 2 (mm) (s) (s) (s) (m/s) (%) (mm) (mm) (%) 400 L 2 80.96 84.19 87.18 1427.5 3.54% 4.8 2.07 3.7 600 L 3 80.96 85.51 87.18 1520.1 2.71% 6.7 2.92 2.6 1000 L 5 80.96 88.64 87.21 1501 1.42% 11.4 4.93 1.4 1800 L 9 80.96 96.36 87.22 1347.4 8.96% 22.8 9.89 9.8/2.7 * * Represents the calibrated error in hours for the case of 1800 L as explained in Section 3.3. The percentage errors in the liquid height for 400 L, 600 L, 1000 L, and 1800 L are 3.7%, 2.6%, 1.4%, and 9.8%, respectively. As expected, in the case of 1800 L, the error is high because the height is above 0.86 L, so the obtained (S + S ) is not accurate. This case represents the second 1 2 case that is explained in Appendix A.2. To address this issue, the total traveled distance was found via parametric CAD software (Inventor Autodesk 201), as illustrated in Figure 7, for the critical case, 1000 L, and 1800 L. From this figure, one can observe that the total traveled distance (S + S ) 1 2 for 1000 L exactly matches the value found in Table 4. By contrast, for 1800 L, the total traveled distance does not exactly match the table. The corrected value for the case of 1800 L from the figure is 21.31 mm, which gives a C of 1383 m/s and height of 9.24 mm. Therefore, the error for 1800 L is LW dramatically reduced to 2.7%. The error in the height estimation might be caused by several factors, such as the theoretical value of the speed of sound in water and air, which mainly varies with the temperature, the surface tension phenomenon, and the estimated area of the liquid container. Acoustics 2020, 2, 366–381  376 of 381  Critical 1000µL 1800µL Acoustics 2020, 2 376 Acoustics 2020, 2, 366–381  376 of 381  Critical 1000µL 1800µL     (a)  (b)  (c)  Figure 7. The CAD results for the wave traveling in the liquid, showing the actual total traveled  distance for three cases: the (a) critical case; (b) 1000 μL case, and (c) 1800 μL case.      The error in the height estimation might be caused by several factors, such as the theoretical  value of the speed of sound in water and air, which mainly varies with the temperature, the surface  (a)  (b)  (c)  tension phenomenon, and the estimated area of the liquid container.  Figure 7. The CAD results for the wave traveling in the liquid, showing the actual total traveled Figure 7. The CAD results for the wave traveling in the liquid, showing the actual total traveled  distance for three cases: the (a) critical case; (b) 1000 L case, and (c) 1800 L case. distance for three cases: the (a) critical case; (b) 1000 μL case, and (c) 1800 μL case.  3.4. Short‐Time Fourier Transform Analysis for Both the Reflected Wave from the Defect (Edge) and the  Liquid  3.4. Short-Time Fourier Transform Analysis for Both the Reflected Wave from the Defect (Edge) and the Liquid The error in the height estimation might be caused by several factors, such as the theoretical  The goal of Short‐Time Fourier Transform Analysis (STFT) is to determine the effect of fluid  value of the speed of sound in water and air, which mainly varies with the temperature, the surface  The goal of Short-Time Fourier Transform Analysis (STFT) is to determine the e ect of fluid existence and fluid volume on the signal frequency. STFT is a useful technique to convert the time  existence tension phen andomenon, fluid volume  and the on esti thema signal ted are frequency a of the .liSTFT quid cont is a ainer. useful  technique to convert the time domain response of the signal into the frequency‐time domain for a selected window. The resolutions  domain response of the signal into the frequency-time domain for a selected window. The resolutions of  time  and frequency are  inversely  proportional;  as  the  frequency  resolution  increases,  the  time  3.4. Short‐Time Fourier Transform Analysis for Both the Reflected Wave from the Defect (Edge) and the  of time and frequency are inversely proportional; as the frequency resolution increases, the time resolution  decreases,  and  vice  versa  [32].  The  longer  the  window  is,  the  higher  the  frequency  Liquid  resolution decreases, and vice versa [32]. The longer the window is, the higher the frequency resolution resolution that will be obtained with a lower time resolution [33]. For this reason, a trade‐off between  that will be obtained with a lower time resolution [33]. For this reason, a trade-o between frequency The goal of Short‐Time Fourier Transform Analysis (STFT) is to determine the effect of fluid  frequency resolution and time resolution should be carefully implemented depending on which is  resolution and time resolution should be carefully implemented depending on which is more important existence and fluid volume on the signal frequency. STFT is a useful technique to convert the time  more important for a particular study. In this study, we utilized MATLAB (signal processing) to  for a particular study. In this study, we utilized MATLAB (signal processing) to obtain the STFT domain response of the signal into the frequency‐time domain for a selected window. The resolutions  obtain the STFT for the RWE (Reflected Wave from the Edge) and RWL (Reflected Wave from the  for the RWE (Reflected Wave from the Edge) and RWL (Reflected Wave from the Liquid) windows. of  time  and frequency are  inversely  proportional;  as  the  frequency  resolution  increases,  the  time  Liquid) windows. The time resolution was set to be 1 μs. The settings for the leakage and overlap are  The time resolution was set to be 1 s. The settings for the leakage and overlap are 1% and 99%, resolution  decreases,  and  vice  versa  [32].  The  longer  the  window  is,  the  higher  the  frequency  1%  and  99%,  respectively.  Figure  8  represents  the  STFT  of  the  RWE  and  RWL  for  all  cases.  For  respectively. Figure 8 represents the STFT of the RWE and RWL for all cases. For instance, Figure 8a1,b1 resolution that will be obtained with a lower time resolution [33]. For this reason, a trade‐off between  instance, Figure 8a1,b1 show the STFT results for the empty case obtained for the RWE and RWL,  show the STFT results for the empty case obtained for the RWE and RWL, respectively. Figure 8a2,b2 frequency resolution and time resolution should be carefully implemented depending on which is  respectively.  Figure  8a2,b2  show  the  STFT  for  400 μL  cases  obtained  for  the  RWE  and  RWL,  show the STFT for 400 L cases obtained for the RWE and RWL, respectively, and so on. The x-axis more important for a particular study. In this study, we utilized MATLAB (signal processing) to  respectively, and so on. The x‐axis represents the time in μs, and the y‐axis represents the frequency  represents the time in s, and the y-axis represents the frequency in MHz. The light-yellow(-dB), obtain the STFT for the RWE (Reflected Wave from the Edge) and RWL (Reflected Wave from the  in MHz. The light‐yellow(‐dB), which is close to 0 dB, represents the dominant frequency components  which is close to 0 dB, represents the dominant frequency components of the signal at a specific time. Liquid) windows. The time resolution was set to be 1 μs. The settings for the leakage and overlap are  of the signal at a specific time. If the yellow color becomes darker or changes to blue in a particular  If the yellow color becomes darker or changes to blue in a particular region, it indicates that a lower 1%  and  99%,  respectively.  Figure  8  represents  the  STFT  of  the  RWE  and  RWL  for  all  cases.  For  region, it indicates that a lower frequency component of the signal is localized.  frequency component of the signal is localized. instance, Figure 8a1,b1 show the STFT results for the empty case obtained for the RWE and RWL,  respectively.  Figure  8a2,b2  show  the  STFT  for  400 μL  cases  obtained  for  the  RWE  and  RWL,  respectively, and so on. The x‐axis represents the time in μs, and the y‐axis represents the frequency  in MHz. The light‐yellow(‐dB), which is close to 0 dB, represents the dominant frequency components  of the signal at a specific time. If the yellow color becomes darker or changes to blue in a particular  region, it indicates that a lower frequency component of the signal is localized.  (a1)  (b1)  Figure 8. Cont. (a1)  (b1)  Acoustics 2020, 2 377 Acoustics 2020, 2, 366–381  377 of 381  Fi t L k R l i h W SdL k R lihW (b2)  (a2)  (a3)  (b3)  (a4)  (b4)  (a5)  (b5)  Figure Figure8. 8. ((aa)) Short-T Short‐Time ime Fourier Fourier TTransform ransform for  forthe  ther reflection eflection fr from om edge  edge/co /corner rnerin inall  allcases:  cases: ((a1 a1)) empty empty, ,  (a2 (a2 ))400  400 μ L,L, ( a3 (a3 ) ) 600  600 μ L,L, (a4 (a4 ) 100 ) 1000 0  μ L,L, and  and (a5 (a5 ) 1800 ) 1800 L; μL; (b )(b STFT ) STFT for for the the reflection  reflection from from the the liquid  liqu inid all in  cases: (b1) empty, (b2) 400 L, (b3) 600 L, (b4) 1000 L, and (b5) 1800 L. all cases: (b1) empty, (b2) 400 μL, (b3) 600 μL, (b4) 1000 μL, and (b5) 1800 μL.  Acoustics 2020, 2 378 From Figure 8a1–a5, it can be observed that the central frequency of the RWE for all cases is lower than in the case of the empty container. A slight change in the fundamental frequency as the volume of liquid increases can be seen. Besides, multiple reflections from liquid appear before and after the RWE as the volume of liquid increases. From Figure 8b1–b5, it can be observed the first leaky Rayleigh wave, at the first edge/corner of the container, with a frequency of 3.5 to 4 MHz, occurs at a time between 80 s and 82 s for all cases except the empty container. The second leaky Rayleigh wave, at the end edge/corner of the container, appears at a time between 86 s and 88 s. The first leaky Rayleigh wave and the second leaky Rayleigh wave are denoted with solid red arrows and dashed red arrows, respectively, in Figure 8b2. Additionally, multiple reflections from the top surface of the liquid appear as the light-yellow color between or after the two Leaky Rayleigh waves based on the liquid volume, as previously explained in Section 3.2. Note that the first and second Leaky Rayleigh waves occurred at the same time plots (Figure 8b2–b5). 4. Conclusions In this paper, the impact of liquid presence on a solid surface on surface acoustic waves (SAWs) was experimentally investigated. Additionally, with the aid of the fact that when a SAW interacts with a liquid as it is traveling along the solid surface, some of its energy is transmitted through the liquid and some energy is reflected, the liquid height can be accurately estimated via analyzing the time domain response of the received signal. The results show that the peak-to-peak amplitude of the received SAW signal is dramatically reduced when liquid is present on the solid surface by almost 62.5% compared to the free surface (no liquid). With an increase in liquid volume, the peak-to-peak amplitude is slightly decreased, which indicates that the SAW is more sensitive to the area being covered by a liquid than the volume of the liquid. The results further show the capability of utilizing SAW to precisely measure the liquid height, with a small error that does not exceed 10% in all the tested cases in this study. Author Contributions: Conceptualization, H.A. and R.G.; methodology, H.A. and R.G.; software, H.A.; validation, H.A.; formal analysis, H.A.; investigation, H.A.; resources, R.G.; data curation, H.A. and R.G.; writing—original draft preparation, H.A.; writing—review and editing, R.G.; visualization, H.A.; supervision, R.G.; project administration, R.G.; funding acquisition, R.G. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest. Appendix A Appendix A.1 Finding the Refraction Angle To find the refraction angle at the solid–fluid interface ( ), Equation (A1) can be utilized. The theoretical value of C at a temperature of 20 C, C , and  are 1480 m/s, 2975.3 m/s, and 90 , Lw LR LR respectively. By substituting these values into Snell’s law, as illustrated in Equation (A1), we get: C sin( ) = C sin( ) (A1) LR 1 Lw R 2975.3 sin( ) = 1480 sin(90) (A2) = 29.83 (A3) The critical incident angle of the liquid can be obtained by substituting  = 90 , C , and C air Lw air into Snell’s law, as in Equation (A4): C sin( ) = C sin( ) (A4) air air LW critcal Acoustics 2020, 2 379 343 sin(90) = 1480 sin( ) (A5) critical = 13.40 (A6) critical Appendix A.2 The Derivation Equation for the Second Case when h > 0.86 L Equation (6) can no longer be applicable if the incident wave reflected from the liquid–air interface will hit the container edge at some height before it is reflected toward the solid surface with an incident angle of  , and it travels a distance of S . Therefore, the total distance traveled in the liquid is S + S + 3 3 1 2 S , as shown in Figure 2b. The angle  is measured by substituting the longitudinal velocity of the PLA 3 3 container, which is experimentally determined to be between 2200 m/s and 2300 m/s, depending on various conditions [31], the velocity of the liquid, and angle  into Snell’s law. The obtained angle 2 3 is 50.7 when using the velocity of 2300 m/s. The error in the height measurement will be high if Equation (6) is utilized, since the S value is neglected. Hence, a modification of Equation (6) should be implemented to improve the accuracy of the height measurement. Through analyzing the vector (S , S , S ) components with trigonometry as 1 2 3 illustrated in Figure 2b, the imaginary part (y) and the real part (x) are derived in terms of  ,  , and L 1 3 as: y : S cos  S cos  S sin  = 0 (A7) 1 1 2 1 3 3 x : S sin  + S sin  S cos  = L S cos  (A8) 2 3 3 3 3 1 1 1 By substituting S = h/cos into the previous equations and solving for S and S in terms of h,  , 1 1 2 3 1 , and L, we obtain: h sin y : S = S (A9) 2 3 cos  cos 1 1 L h x : S = (A10) sin  cos 1 1 Solving the two equations, S can be found as: 2h (L  cot  ) S = (A11) sin If h = 10 mm, L = 8 mm,  = 29.83 , and  = 50.7 and substituting these values into 1 3 Equations (5), (A10), and (A11), we get S , S , and S equal to 11.52 mm, 4.55 mm, and 7.816 mm, 1 2 3 respectively. It can be observed that S < S + S , which verifies the fact that Equation (6) cannot be 1 2 3 applicable when h > 0.86 L. 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Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Journal

AcousticsMultidisciplinary Digital Publishing Institute

Published: Jun 6, 2020

Keywords: surface acoustic wave; attenuation; leaky Rayleigh wave; Short-Time Fourier Transform Analysis

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