3. When the amount of water mist of large particles was constant, the gas removal rate increased with the electric power input to the transducer and the amount of water mist of small particles for the ranges of input power and amount examined in this study.

water mist of small particles is 0.27 cm3/s, and driving frequency is 19.8 kHz.

approximately 3 μm) generated using a water spray system.

The following findings were obtained.

0

50

Removal rate [%]

100

ultrasonic waves and water mist.

particles were simultaneously used.

**3.4 Summary**

#### **3.3.5 Examination of gas removal efficiency with different initial gas concentrations**

To examine the gas removal efficiency with different initial concentrations of lemon-odor gas, a gas removal experiment was performed. In this experiment, the area of the base of the petri dish into which the lemon oil was placed was changed to vary the amount of generated gas. The experimental procedure was the same as before.

Figure 21 shows the experimental results, where the ordinate represents the concentration of lemon-odor gas and the abscissa represents the elapsed time, with the initial gas concentration as a parameter. In all cases, the gas concentration remained almost constant between -180 and 0 s, during which no ultrasonic waves were irradiated. When ultrasonic waves and the water mist were generated at 0 s, however, the gas concentration sharply decreased.

Next, a similar experiment was carried out to obtain the gas removal rate with different initial gas concentrations. The gas removal rate was calculated from the experimental results using eq. (15). Figure 22 shows the results, where the ordinate represents the gas removal rate and the abscissa represents the initial gas concentration. When the amounts of water mist of small and large particles and the input electric power were constant, the gas removal rate tended to increase with the initial gas concentration in the range examined in this experiment. This was considered to be because the higher the gas concentration, the greater the number of opportunities for the water mist to absorb gas particles.

Fig. 21. Relationship between elapsed time and gas concentration. The input electric power is 50 W, the amount of water mist of large particles is 2.78 cm3/s, the amount of water mist of small particles is 0.27 cm3/s, and the driving frequency is 19.8 kHz.

Fig. 22. Relationship between initial gas concentration and removal rate. The input electric power is 50 W, the amount of water mist of large particles is 2.78 cm3/s, the amount of water mist of small particles is 0.27 cm3/s, and driving frequency is 19.8 kHz.

## **3.4 Summary**

128 Ultrasonic Waves

Figure 21 shows the experimental results, where the ordinate represents the concentration of lemon-odor gas and the abscissa represents the elapsed time, with the initial gas concentration as a parameter. In all cases, the gas concentration remained almost constant between -180 and 0 s, during which no ultrasonic waves were irradiated. When ultrasonic waves and the water

Next, a similar experiment was carried out to obtain the gas removal rate with different initial gas concentrations. The gas removal rate was calculated from the experimental results using eq. (15). Figure 22 shows the results, where the ordinate represents the gas removal rate and the abscissa represents the initial gas concentration. When the amounts of water mist of small and large particles and the input electric power were constant, the gas removal rate tended to increase with the initial gas concentration in the range examined in this experiment. This was considered to be because the higher the gas concentration, the greater

Fig. 21. Relationship between elapsed time and gas concentration. The input electric power is 50 W, the amount of water mist of large particles is 2.78 cm3/s, the amount of water mist

of small particles is 0.27 cm3/s, and the driving frequency is 19.8 kHz.

**3.3.5 Examination of gas removal efficiency with different initial gas concentrations**  To examine the gas removal efficiency with different initial concentrations of lemon-odor gas, a gas removal experiment was performed. In this experiment, the area of the base of the petri dish into which the lemon oil was placed was changed to vary the amount of

generated gas. The experimental procedure was the same as before.

mist were generated at 0 s, however, the gas concentration sharply decreased.

the number of opportunities for the water mist to absorb gas particles.

In this section, I examined the effect on the increase in gas removal rate obtained when a low-hydrophilicity gas was absorbed and aggregated by irradiating aerial ultrasonic waves onto water mist of large particles (average particle diameter, approximately 60 μm) formed by the vibration of the plate and water mist of small particles (average particle diameter, approximately 3 μm) generated using a water spray system.

The following findings were obtained.

Intense Aerial Ultrasonic Source and Removal of Unnecessary Gas by the Source 131

Ito, Y. & Takamura, E. (2010). Removal of Liquid in a Long Pore Opened at Both Ends Using

Kobayashi, M., Kamata, C. & Ito, K. (1997). Cold Model Experiments of Gas Removal from

Lang, R. J. (1962). Ultrasonic Atomization of Liquids. *The Journal of the Acoustical Society of*

Miura, H. (1994). Aerial Ultrasonic Vibration Source using a Square Plate Vibrating in a

Miura, H., & Honda, Y. (2002). Aerial Ultrasonic Source Using a Striped Mode Transverse

Miura, H. (2003). Eggshell Cutter Using Ultrasonic Vibration. *Japanese Journal of Applied*

Miura, H. (2004). Promotion of Sedimentation of Dispersed Fine Particles Using Underwater

Miura, H., Takata, M., Tajima, D. & Tsuyuki, K. (2006). Promotion of Methane Hydrate

Miura, H. (2007a). Removal of Unnecessary Gas by Spraying Water Particles Formed by

Miura, H. (2007b). Atomization of High-Viscosity Materials by One Point Convergence of

Miura, H. (2008). Vibration Characteristics of Stepped Horn Joined Cutting Tip Employed in

Miura, H. & Ishikawa, H. (2009). Aerial Ultrasonic Source Using Stripes-Mode Transverse

Onishi, Y. & Miura, H. (2005). Convergence of Sound Waves Radiated from Aerial

Ueha, S., Maehara, N. & Mori,E. (1985). Mechanism of Ultrasonic Atomization using a

*Japan (ISIJ) International,* Vol. 37, No. 1, (January 1997), pp. 9-1 5.

07HE22, (July 2010), pp. 07HE22-1-6.

*America*, Vol. 34, No. 1, (January 1962), pp. 6-8.

(September 1994), pp. 677-684.[in Japanese]

Vol. 45, No. 5B, (May 2006), pp.4816-4823.

47, No. 5, (May 2008), pp. 4282-4286.

(January 1985), pp. 21-26.

48, 07GM10, (July 2009), pp. 07GM10-1-4.

2004), pp. 2838-2839.

2007), pp. 4926-4930.

09-017.

4688.

Vol. 41, Part 1, No. 5B, (May 2002), pp. 3223-3227.

*Physics,* Vol. 42, Part 1, No.5B, (May 2003), pp. 2996-2999.

High-Intensity Aerial Ultrasonic Waves. *Japanese Journal of Applied Physics*, Vol. 49,

Molten Metal by an Irradiation of Ultrasonic Waves. *The Iron and Steel Institute of*

Transverse Lattice-Mode. *The Journal of the Acoustical Society of Japan*, Vol. 50, No. 9,

Vibrating Plate with Two Driving Frequencies. *Japanese Journal of Applied Physics,*

Ultrasonic Wave. *Japanese Journal of Applied Physics,* Vol. 43, Part 1, No. 5B, (May

Dissociation by Underwater Ultrasonic Wave. *Japanese Journal of Applied Physics,*

Aerial Ultrasonic Waves. *Japanese Journal of Applied Physics,* Vol. 46, No. 7B, (July

Sound Waves Radiated from an Aerial Ultrasonic Source using a Transverse Vibrating Plate. *The 19th International Congress on Acoustics*, (September 2007), ULT-

Circular Cutting Using Ultrasonic Vibration. *Japanese Journal of Applied Physics,* Vol.

Vibrating Plate with Jutting Driving Point. *Japanese Journal of Applied Physics,* Vol.

Ultrasonic Source Using Square Transverse Vibrating Plate with Several Reflective Boards. *Japanese Journal of Applied Physics,* Vol. 44, No. 6B, (June 2005), pp. 4682-

Multipinhole Plate. *Journal of the Acoustical Society of Japan (E)*, Vol. 6, No. 1,

From these results, it was found that a gas can be effectively removed by irradiating ultrasonic waves onto water mist of both large and small particles.

## **4. Conclusion**

In this chapter, I described a method of designing square plates vibrating flexurally in the lattice mode that can be used as an intense aerial ultrasonic source, as well as the vibration mode of the fabricated plates. The distributions of the vibration displacement of the fabricated plates and the sound pressure near the plate surface were also described. In addition, the validity of the ultrasonic source was verified by theoretically and experimentally determining the directivity of the sound waves radiated from the vibrating plates into remote acoustic fields.

As an application of intense aerial ultrasonic waves, the enhancement of the removal of an unnecessary gas was examined. It was demonstrated that up to 90% of the gas was removed when aerial ultrasonic waves were irradiated onto water mist of large particles (average particle diameter, approximately 60 μm) formed by the flexural vibration of the plate and water mist of small particles (average particle diameter, approximately 3 μm) separately generated using a water spray system.

Thus, the use of aerial ultrasonic energy to remove unwanted gases appears to be promising; however, many unclear points still remain. Their clarification is expected to lead to an expansion in the range of applications of ultrasonic energy.

## **5. References**

4. When the amount of water mist of small particles was constant, the gas removal rate tended to increase with the electric power input to the transducer and the amount of

5. When the two kinds of water mist of large and small particles were used and subjected to ultrasonic irradiation, the gas removal rate increased with the initial gas concentration. 6. The gas removal rate reached approximately 90% when the amounts of water mist of small and large particles were 0.27 and 2.78 cm3/s, respectively, and the electric power

From these results, it was found that a gas can be effectively removed by irradiating

In this chapter, I described a method of designing square plates vibrating flexurally in the lattice mode that can be used as an intense aerial ultrasonic source, as well as the vibration mode of the fabricated plates. The distributions of the vibration displacement of the fabricated plates and the sound pressure near the plate surface were also described. In addition, the validity of the ultrasonic source was verified by theoretically and experimentally determining the directivity of the sound waves radiated from the vibrating

As an application of intense aerial ultrasonic waves, the enhancement of the removal of an unnecessary gas was examined. It was demonstrated that up to 90% of the gas was removed when aerial ultrasonic waves were irradiated onto water mist of large particles (average particle diameter, approximately 60 μm) formed by the flexural vibration of the plate and water mist of small particles (average particle diameter, approximately 3 μm) separately

Thus, the use of aerial ultrasonic energy to remove unwanted gases appears to be promising; however, many unclear points still remain. Their clarification is expected to lead

Asami, T. & Miura, H. (2010). Longitudinal Vibration Characteristics Required to Cut a

Asami, T. & Miura, H. (2011). Vibrator Development for Hole Machining by Ultrasonic

David, J. & Cheeke, N. (2002). *Fundamentals and applications of ultrasonic waves,* CRC Press,

Ito, Y. (2005). Experimental Investigation of Deflection of High-Speed Water Current with

Circle by Ultrasonic Vibration. *Japanese Journal of Applied Physics,* Vol. 49, 07HE23,

Longitudinal and Torsional Vibration. *Japanese Journal of Applied Physics,* Vol. 50,

Aerial Ultrasonic Waves. *Japanese Journal of Applied Physics*, Vol. 44, Part 1, No. 6B,

water mist of large particles.

input to the transducer was 50 W.

plates into remote acoustic fields.

generated using a water spray system.

(July 2010), pp. 07HE23-1-7

(June 2005), pp. 4669-4673.

07HE31, (July 2010), pp. 07HE31-1-9

ISBN 0-8493-0130-0, Florida, USA.

**4. Conclusion**

**5. References**

ultrasonic waves onto water mist of both large and small particles.

to an expansion in the range of applications of ultrasonic energy.

**7**

*Algeria*

**Application of Pulsed**

*University Ibn Khaldoun of Tiaret*

N. Sad Chemloul, K. Chaib and K. Mostefa

 **Ultrasonic Doppler Velocimetry to the**

**Simultaneous Measurement of Velocity**

 **and Concentration Profiles in Two Phase Flow**

The improvement of knowledge which governs the transport of the solid-liquid suspensions is the subject of many works having generally led to empirical or semi-empirical models which are valid only for specific conditions. Research carried out on solid-liquid suspensions has investigated the continuous phase and particularly the influence of turbulence modulation. In the works by Elghobashi and Truesdell (1993), Michaelides and Stock (1989), Owen (1969), and Parthasarathy and Faeth (1990a, 1990b), dissipation or production of turbulent kinetic energy in the continuous phase were reported. The effect of particles on the carrier flow turbulence was investigated numerically by Varaksin and Zaichik (2000) and, Lei (2000). Recently PUDV (pulsed ultrasonic Doppler velocimetry) was applied to study fluid flow alone or with solid particles by Takeda (1995), Aritomi et al. (1996), Nakamura (1996), Rolland and Lemmin (1996, 1997), Cellino and Graf (2000), Brito et al (2001), Eckert and Gerbeth (2002), Kikura et al. (1999), Kikura et al. (2004), Xu (2003), Alfonsi et al. (2003). Note that the measurement techniques cited

The aim of this experimental chapter is the simultaneous measurement of the local parameters which are the velocity and the concentration fields of the solid particles in flows in a horizontal pipe. The difference between our application of PUDV and those cited in the above references resides in the use of a new measurement approach of the local concentration of the solid particles. This approach consists of the representation of the local concentration profile by the ratio of the number of solid particles crossing the measurement volume, to the number of solid particles crossing the control volume. PUDV technique was selected rather than hot wire or film, or Laser, or the PIV technique, because the first would be destroyed by the particles, and with the second the ultrasonic signal is more attenuated when the volumetric concentration CV of particles increases. The third technique as reported

The working principle of pulsed ultrasound Doppler velocimetry is to detect and process many ultrasonic echoes issued from pulses reflected by micro particles contained in a

in the above references are limited by the nature of the suspensions.

by Jensen (2004) requires many conditions for its application.

**1. Introduction**

**2. Experiment**

Yamane, H., Ito, Y., & Kawamura, M. (1983). Sound Radiation from Rectangular Plate Vibrating in Stripes Mode. *The Journal of the Acoustical Society of Japan*, Vol. 39, No. 6, (June 1983), pp. 380-387.[in Japanese]

## **Application of Pulsed Ultrasonic Doppler Velocimetry to the Simultaneous Measurement of Velocity and Concentration Profiles in Two Phase Flow**

N. Sad Chemloul, K. Chaib and K. Mostefa *University Ibn Khaldoun of Tiaret Algeria*

## **1. Introduction**

132 Ultrasonic Waves

Yamane, H., Ito, Y., & Kawamura, M. (1983). Sound Radiation from Rectangular Plate

(June 1983), pp. 380-387.[in Japanese]

Vibrating in Stripes Mode. *The Journal of the Acoustical Society of Japan*, Vol. 39, No. 6,

The improvement of knowledge which governs the transport of the solid-liquid suspensions is the subject of many works having generally led to empirical or semi-empirical models which are valid only for specific conditions. Research carried out on solid-liquid suspensions has investigated the continuous phase and particularly the influence of turbulence modulation. In the works by Elghobashi and Truesdell (1993), Michaelides and Stock (1989), Owen (1969), and Parthasarathy and Faeth (1990a, 1990b), dissipation or production of turbulent kinetic energy in the continuous phase were reported. The effect of particles on the carrier flow turbulence was investigated numerically by Varaksin and Zaichik (2000) and, Lei (2000). Recently PUDV (pulsed ultrasonic Doppler velocimetry) was applied to study fluid flow alone or with solid particles by Takeda (1995), Aritomi et al. (1996), Nakamura (1996), Rolland and Lemmin (1996, 1997), Cellino and Graf (2000), Brito et al (2001), Eckert and Gerbeth (2002), Kikura et al. (1999), Kikura et al. (2004), Xu (2003), Alfonsi et al. (2003). Note that the measurement techniques cited in the above references are limited by the nature of the suspensions.

The aim of this experimental chapter is the simultaneous measurement of the local parameters which are the velocity and the concentration fields of the solid particles in flows in a horizontal pipe. The difference between our application of PUDV and those cited in the above references resides in the use of a new measurement approach of the local concentration of the solid particles. This approach consists of the representation of the local concentration profile by the ratio of the number of solid particles crossing the measurement volume, to the number of solid particles crossing the control volume. PUDV technique was selected rather than hot wire or film, or Laser, or the PIV technique, because the first would be destroyed by the particles, and with the second the ultrasonic signal is more attenuated when the volumetric concentration CV of particles increases. The third technique as reported by Jensen (2004) requires many conditions for its application.

## **2. Experiment**

The working principle of pulsed ultrasound Doppler velocimetry is to detect and process many ultrasonic echoes issued from pulses reflected by micro particles contained in a

Application of Pulsed Ultrasonic Doppler Velocimetry to

**2.2 Ultrasonic measurement system of the velocity profiles**

m/s to 2.5 m/s.

the Simultaneous Measurement of Velocity and Concentration Profiles in Two Phase Flow 135

This study was performed using water as the continuous phase and glass beads for solid particles. The particles are spherical with a 5% sphericity defect and density of 2640 kg/m3. Four samples of different particle size distributions were tested. The volume-averaged mean particle diameters dp corresponding to these samples are 0.27, 0.3, 0.4, and 0.7 mm. These particles were chosen to be larger than the Kolmogorov length scale , estimated to 206.6 m near the wall. The particle diameter is ranging between 1.30 and 3.38. The volumetric concentrations (Cv) of the glass beads used in the suspension are 0.5%, 1%, 1.5% and 2%, and were determined from the volume of the flow circuit. Performed measurements within this work consider a two way coupling, i.e., taking into account the effects of the particles on the carrier fluid and vice versa. The classification of the suspension flow used is made according to Sato (1996), Elghobashi (1994) and Crowe, et al. (1996) who proposed the particle volume fractions as the criterion of classification. The particle volume fractions are ranging between 1.25 x10-3 and 5x10-3. Fine starch particles with 6 m of diameter and density of 1530 kg/m3 were used as a tracer. The maximum concentration of the starch was fixed at 3% in order to reduce the attenuation of the Doppler signal. The flow mean velocity Umoy is ranging from 1

The method used for measurement local velocity of the large particles (larger than the wavelength of the ultrasonic wave) is based on a combination of the measurement technique PUDV (7) (type ECHOVAR CF8) used in medical physics, and a data processor (9). The technical specifications of the velocimeter are: emission frequency 8 MHz, pulse durations 0.5 s, 1 s, 2 s, and pulse repetition frequency 64 s and 32 s. The maximum measurable

The position adjustment of the measurement volume is done by time step of 0.5 s between the emission and reception of the ultrasonic wave. This time step corresponds to the penetration depth of the measurement volume of 0.37 mm for an angle of 67° ( angle between the internal pipe wall and the direction of the propagation of the ultrasonic waves). The value of is nearly equal to that determined by the calibration of the ultrasonic transducer (67.4°). The dimensions of the cylindrical measurement volume are the same as

In this experimental study, the signal is emitting and receiving by the same ultrasonic transducer, in this case the velocity U (axial velocity component) of the solid particles

with fD the Doppler shift frequency, fe the emitted frequency by the transducer, c speed of the sound in the water, and the angle between the ultrasonic beam and the pipe axis.

The use of the PUDV technique for the solid-liquid suspensions remains however, limited by the concentration of the solid particles. Indeed, the preliminary study results show that the concentration of the solid particles and depth of the measurement volume affect the ultrasonic signal. Figure 2 shows that for a concentration higher than 2.5%, the attenuation

D e cf U =

2f cosθ (1)

distance of these two pulse repetition frequency are respectively 48 mm and 24 mm.

those of the ultrasonic transducer, diameter of 2 mm and length of 0.8 mm.

determined from the Doppler frequency is:

flowing liquid. A single transducer emits the ultrasonic pulses and receives the echoes. By sampling the incoming echoes at the same time relative to the emission of the pulses, the variation of the positions of scatterers are measured and therefore their velocities. The measurement of the time lapse between the emission of ultrasonic bursts and the reception of the pulse (echo generated by particles flowing in the liquid) gives the position of the particles. By measuring the Doppler frequency in the echo as a function of time shifts of these particles, a velocity profile after few ultrasonic emissions is obtained.

In this study, PUDV technique originally applied in the medical field is used only for the emission and the reception of the ultrasonic signal. This technique was combined with a data processor for the flow measurement of solid-liquid suspension. This combination allows the determination of a local velocity and a local concentration of the solid particles larger than the wavelength of the ultrasonic wave.

#### **2.1 Flow circuit**

The flow circuit (Fig. 1a.) consists of a closed loop made of glass pipes with an internal diameter D of 20 mm. The flow is driven by a variable speed centrifugal pump (1). The suspension is kept at a constant temperature by the heat exchanger (2) during measurement. The test section (4) (for detail see Fig 1b), realized in a Plexiglas box which is 150 mm long, 100 mm wide, and 50 mm high, was located at 75D downstream of the pump where the flow was fully-developed. Plexiglas was chosen in order to reduce the reflection of the ultrasonic beam when it crosses the wall. The pressure differential along the test pipe given by two differential pressure transducer (3) allows the determination of the wall shear stress.

Fig. 1. a) Flow circuit: 1 pump, 2 heat exchanger, 3 differential pressure transducer, 4 test section, 5 tank of suspension; b) Detail of the test section 4: ( ) glass pipe, ( ) Plexiglas box, ( ) Ultrasonic transducer; c) Ultrasonic measurement with acquisition and treatment system: 6 displacement system of the measurement volume, 7 ultrasonic Doppler velocimeter (ECHOVAR CF8, ALVAR), 8 digital storage oscilloscope, 9 data processor (plurimat S), 10 computer

flowing liquid. A single transducer emits the ultrasonic pulses and receives the echoes. By sampling the incoming echoes at the same time relative to the emission of the pulses, the variation of the positions of scatterers are measured and therefore their velocities. The measurement of the time lapse between the emission of ultrasonic bursts and the reception of the pulse (echo generated by particles flowing in the liquid) gives the position of the particles. By measuring the Doppler frequency in the echo as a function of time shifts of

In this study, PUDV technique originally applied in the medical field is used only for the emission and the reception of the ultrasonic signal. This technique was combined with a data processor for the flow measurement of solid-liquid suspension. This combination allows the determination of a local velocity and a local concentration of the solid particles

The flow circuit (Fig. 1a.) consists of a closed loop made of glass pipes with an internal diameter D of 20 mm. The flow is driven by a variable speed centrifugal pump (1). The suspension is kept at a constant temperature by the heat exchanger (2) during measurement. The test section (4) (for detail see Fig 1b), realized in a Plexiglas box which is 150 mm long, 100 mm wide, and 50 mm high, was located at 75D downstream of the pump where the flow was fully-developed. Plexiglas was chosen in order to reduce the reflection of the ultrasonic beam when it crosses the wall. The pressure differential along the test pipe given by two differential pressure transducer (3) allows the determination of

Fig. 1. a) Flow circuit: 1 pump, 2 heat exchanger, 3 differential pressure transducer, 4 test section, 5 tank of suspension; b) Detail of the test section 4: ( ) glass pipe, ( ) Plexiglas box, ( ) Ultrasonic transducer; c) Ultrasonic measurement with acquisition and treatment

system: 6 displacement system of the measurement volume, 7 ultrasonic Doppler velocimeter (ECHOVAR CF8, ALVAR), 8 digital storage oscilloscope, 9 data processor

these particles, a velocity profile after few ultrasonic emissions is obtained.

larger than the wavelength of the ultrasonic wave.

**2.1 Flow circuit**

the wall shear stress.

(plurimat S), 10 computer

This study was performed using water as the continuous phase and glass beads for solid particles. The particles are spherical with a 5% sphericity defect and density of 2640 kg/m3. Four samples of different particle size distributions were tested. The volume-averaged mean particle diameters dp corresponding to these samples are 0.27, 0.3, 0.4, and 0.7 mm. These particles were chosen to be larger than the Kolmogorov length scale , estimated to 206.6 m near the wall. The particle diameter is ranging between 1.30 and 3.38. The volumetric concentrations (Cv) of the glass beads used in the suspension are 0.5%, 1%, 1.5% and 2%, and were determined from the volume of the flow circuit. Performed measurements within this work consider a two way coupling, i.e., taking into account the effects of the particles on the carrier fluid and vice versa. The classification of the suspension flow used is made according to Sato (1996), Elghobashi (1994) and Crowe, et al. (1996) who proposed the particle volume fractions as the criterion of classification. The particle volume fractions are ranging between 1.25 x10-3 and 5x10-3. Fine starch particles with 6 m of diameter and density of 1530 kg/m3 were used as a tracer. The maximum concentration of the starch was fixed at 3% in order to reduce the attenuation of the Doppler signal. The flow mean velocity Umoy is ranging from 1 m/s to 2.5 m/s.

## **2.2 Ultrasonic measurement system of the velocity profiles**

The method used for measurement local velocity of the large particles (larger than the wavelength of the ultrasonic wave) is based on a combination of the measurement technique PUDV (7) (type ECHOVAR CF8) used in medical physics, and a data processor (9). The technical specifications of the velocimeter are: emission frequency 8 MHz, pulse durations 0.5 s, 1 s, 2 s, and pulse repetition frequency 64 s and 32 s. The maximum measurable distance of these two pulse repetition frequency are respectively 48 mm and 24 mm.

The position adjustment of the measurement volume is done by time step of 0.5 s between the emission and reception of the ultrasonic wave. This time step corresponds to the penetration depth of the measurement volume of 0.37 mm for an angle of 67° ( angle between the internal pipe wall and the direction of the propagation of the ultrasonic waves). The value of is nearly equal to that determined by the calibration of the ultrasonic transducer (67.4°). The dimensions of the cylindrical measurement volume are the same as those of the ultrasonic transducer, diameter of 2 mm and length of 0.8 mm.

In this experimental study, the signal is emitting and receiving by the same ultrasonic transducer, in this case the velocity U (axial velocity component) of the solid particles determined from the Doppler frequency is:

$$\mathbf{U} = \frac{\mathbf{c}\mathbf{f}\_{\rm D}}{2\mathbf{f}\_{\rm e}\cos\theta} \tag{1}$$

with fD the Doppler shift frequency, fe the emitted frequency by the transducer, c speed of the sound in the water, and the angle between the ultrasonic beam and the pipe axis.

The use of the PUDV technique for the solid-liquid suspensions remains however, limited by the concentration of the solid particles. Indeed, the preliminary study results show that the concentration of the solid particles and depth of the measurement volume affect the ultrasonic signal. Figure 2 shows that for a concentration higher than 2.5%, the attenuation

Application of Pulsed Ultrasonic Doppler Velocimetry to

the power spectral density.

versus the wall distance

have:

spectrum.

the Simultaneous Measurement of Velocity and Concentration Profiles in Two Phase Flow 137

maximum power spectrum were taken into account. The peak amplitude of the power spectra increases with increasing particle diameter; this confirms the difference in energy between the signals coming from the bead glass and those from the starch particles. The separation between the Doppler signals of the continuous phase and large particle is made using two fixed thresholds on the integral of the power spectral density. The higher threshold Ssup and the lower threshold Sinf are respectively given by the following relations:

sup max

  E -E S =E -

E -E S =E +

where Emax and Emin are respectively, the maximal and the minimal value of the integral of

Fig. 3. Doppler power spectrum in the case of glass beads (dp= 0.7 mm, Cv= 1%) and tracer

where K is a constant and the Dirac's impulse. According to the formula of Poisson, we

where X( ) is the Fourier transform of the Doppler signal x(t) . The values treated using the Fourier transform allow to the calculation of the power spectral density P(f) of the Doppler signal from the product of the frequency spectrum and its conjugate. The average frequency Doppler fD is given by the normalized moment of order 1 of the ensemble average

e

<sup>K</sup> x(t) = x(t) (t - ) <sup>f</sup> (3)

<sup>e</sup> x( ) X( ) ( - nf ) (4)

The sampled function x(t) ˆ of the Doppler signal x(t) is given by:

inf min

max min

(2)

max min

3

3

of the signal is about 80% (or 20% of coherent signal), and thus the maximum volumetric concentration of solid particles used in this study was Cv= 2%. Because of the non-uniform distribution of the concentration in the test section, the flow is divided in two regions having the horizontal line passing through the position of the maximum concentration as a boundary. To obtain this boundary line, which corresponds to the great number of the Doppler signal visualised by a digital storage oscilloscope (Fig. 1c), we have scanned the test section by the displacement of the ultrasonic transducer along the vertical diameter. Before each measurement, the boundary line is located to be taken as the first measurement point. The first measurements with a two same ultrasonic transducers (one fixed on the pipe top wall and the other on the pipe bottom wall) shown that at the same position of the measurement volume, the velocity measured presents a difference about 3 - 4 %. For the high concentration, this difference is more significant.

Fig. 2. Signal attenuation function of the distance from the ultrasonic transducer and the volumetric concentration of particle, dp = 0.7 mm

#### **2.2.1 Signal processing**

The treatment of the Doppler signal is done using a data processor associated with the ultrasonic velocimeter. The successive Doppler signals received by the ultrasonic transducer are result from either the same particle reached by successive impulses, or various particles crossing the measurement volume. These signals depend on the particles size, the dimensions of the measurement volume, and the velocity of the particles. To avoid the spectrum overlap phenomenon and thus the loss of information, the output signal of the velocimeter is sampled with a sampling frequency about 5 to 10 times the greatest frequency of the signal spectrum. The numerical data of the sampling process are stored in the memory of the data processor to be treated. The signal processing is made by an elaborate software where frequency domain and Fourier transform were used. Figure 3 shows that the power spectral density obtained from different wall distance have the same trend as that of Gauss with a value correlation coefficient close to 0.97. To satisfy the symmetry condition of the power spectrum, a threshold was fixed, only the values greater than 2/3 of the

of the signal is about 80% (or 20% of coherent signal), and thus the maximum volumetric concentration of solid particles used in this study was Cv= 2%. Because of the non-uniform distribution of the concentration in the test section, the flow is divided in two regions having the horizontal line passing through the position of the maximum concentration as a boundary. To obtain this boundary line, which corresponds to the great number of the Doppler signal visualised by a digital storage oscilloscope (Fig. 1c), we have scanned the test section by the displacement of the ultrasonic transducer along the vertical diameter. Before each measurement, the boundary line is located to be taken as the first measurement point. The first measurements with a two same ultrasonic transducers (one fixed on the pipe top wall and the other on the pipe bottom wall) shown that at the same position of the measurement volume, the velocity measured presents a difference about 3 - 4 %. For the

Fig. 2. Signal attenuation function of the distance from the ultrasonic transducer and the

The treatment of the Doppler signal is done using a data processor associated with the ultrasonic velocimeter. The successive Doppler signals received by the ultrasonic transducer are result from either the same particle reached by successive impulses, or various particles crossing the measurement volume. These signals depend on the particles size, the dimensions of the measurement volume, and the velocity of the particles. To avoid the spectrum overlap phenomenon and thus the loss of information, the output signal of the velocimeter is sampled with a sampling frequency about 5 to 10 times the greatest frequency of the signal spectrum. The numerical data of the sampling process are stored in the memory of the data processor to be treated. The signal processing is made by an elaborate software where frequency domain and Fourier transform were used. Figure 3 shows that the power spectral density obtained from different wall distance have the same trend as that of Gauss with a value correlation coefficient close to 0.97. To satisfy the symmetry condition of the power spectrum, a threshold was fixed, only the values greater than 2/3 of the

high concentration, this difference is more significant.

volumetric concentration of particle, dp = 0.7 mm

**2.2.1 Signal processing**

maximum power spectrum were taken into account. The peak amplitude of the power spectra increases with increasing particle diameter; this confirms the difference in energy between the signals coming from the bead glass and those from the starch particles. The separation between the Doppler signals of the continuous phase and large particle is made using two fixed thresholds on the integral of the power spectral density. The higher threshold Ssup and the lower threshold Sinf are respectively given by the following relations:

$$\begin{cases} \mathbf{S\_{sup}} = \mathbf{E\_{max}} \cdot \frac{\mathbf{E\_{max}} \cdot \mathbf{E\_{min}}}{\mathcal{B}} \\ \mathbf{S\_{inf}} = \mathbf{E\_{min}} + \frac{\mathbf{E\_{max}} \cdot \mathbf{E\_{min}}}{\mathcal{B}} \end{cases} \tag{2}$$

where Emax and Emin are respectively, the maximal and the minimal value of the integral of the power spectral density.

Fig. 3. Doppler power spectrum in the case of glass beads (dp= 0.7 mm, Cv= 1%) and tracer versus the wall distance

The sampled function x(t) ˆ of the Doppler signal x(t) is given by:

$$\hat{\mathbf{x}}(\mathbf{t}) = \mathbf{x}(\mathbf{t}) \sum \mathbf{\hat{s}}(\mathbf{t} \cdot \frac{\mathbf{K}}{\mathbf{f}\_{\mathbf{e}}}) \tag{3}$$

where K is a constant and the Dirac's impulse. According to the formula of Poisson, we have:

$$\hat{\mathbf{x}}(\mathbf{v}) \boxdot \ \boxdot \ \overleftarrow{\boxdot} \ \mathbf{X}(\mathbf{v}) \sum \delta(\mathbf{v} - \mathbf{n} \mathbf{f}\_{\mathbf{e}}) \tag{4}$$

where X( ) is the Fourier transform of the Doppler signal x(t) . The values treated using the Fourier transform allow to the calculation of the power spectral density P(f) of the Doppler signal from the product of the frequency spectrum and its conjugate. The average frequency Doppler fD is given by the normalized moment of order 1 of the ensemble average spectrum.

Application of Pulsed Ultrasonic Doppler Velocimetry to

along the vertical diameter of the test section (Fig. 4).

transducer

**transducer**

the Simultaneous Measurement of Velocity and Concentration Profiles in Two Phase Flow 139

n pt p i i=1

with n the number of the measurement point. The local concentration profile is obtained by the plot of the variation of the ratio Np / Npt versus the depth of the measurement volume

Fig. 5. a) Validation of the method and calibration of the ultrasonic transducer: 1 glass tank of calibration, 2 lateral wall of the tank, 3 ultrasonic transducer, 4 micrometric displacement system of the transducer, 5 plastic disc, 6 Abrasive cloth band or cylindrical metal rods, 7 ultrasonic Doppler velocimeter, 8 digital storage oscilloscope, 9 Data processor (Plurimat S); b) Validation curve of the signal processing method; c) Calibration curve of the ultrasonic

**2.2.3 Validation of the processing signal method and calibration of the ultrasonic**

The validation of the method applied for the signal processing consists of a comparison between the results obtained by the data processor (9) and those of the processing signal system integrated into the medical apparatus (7). For this validation we developed a device illustrated in Fig. 5a, it consists of the plastic disc (5) of 160 mm diameter turning with a variable speed motor, and on which a abrasive cloth band (6) is stuck (in Figure 5a, only the

N = (N ) (7)

$$\overline{\mathbf{f\_D}} = \frac{\sum\_{n=1}^{N} \mathbf{f\_nG(f\_n)}}{\sum\_{n=1}^{N} \mathbf{G(f\_n)}} \tag{5}$$

where N k n n=1 G(f ) = P (f ) <sup>k</sup> and k = 1, 2, 3,...........,N. Considering that the enlargement of the spectrum is due only to the turbulent velocity fluctuations, we can calculate the normalized moment of second order of the energy spectrum integral associated with the Doppler signals. This moment with a Gaussian trend represents the turbulent intensity given by the relation:

$$\sqrt{\mathbf{f\_D^2}} = \left[\sum\_{n=1}^{N} (\mathbf{f\_n} \cdot \overline{\mathbf{f\_d}})^2 \mathbf{G(f\_n)} / \sum\_{n=1}^{N} \mathbf{G(f\_n)}\right]^{1/2} \tag{6}$$

#### **2.2.2 Measurement method of the local concentration profile**

This method consists of determining the ratio of the number of particles Np crossing the measurement volume to the total number of particles Npt crossing the control volume. This control volume is obtained by the displacement of the measurement volume along the vertical diameter of the test section (Fig. 4).

Fig. 4. Determination of the concentration profile: (-) measurement volume Np, (---) control volume Npt , (-..-) test section.

The numbers of particles Np and Npt are obtained by counting the number of the Doppler signal respectively in the volume measurement and in the control volume. For this counting made for each measurement point of the particle velocity, two thresholds are fixed, one on the amplitude of the Doppler signal and the other on the integral of the power spectral density. The total number of particles Npt is given by:

n=1 N

D

where

relation:

N k n n=1

f =

N n

n=1

spectrum is due only to the turbulent velocity fluctuations, we can calculate the normalized moment of second order of the energy spectrum integral associated with the Doppler signals. This moment with a Gaussian trend represents the turbulent intensity given by the

N N

D nd n n n=1 n=1

This method consists of determining the ratio of the number of particles Np crossing the measurement volume to the total number of particles Npt crossing the control volume. This control volume is obtained by the displacement of the measurement volume along the

Fig. 4. Determination of the concentration profile: (-) measurement volume Np, (---) control

The numbers of particles Np and Npt are obtained by counting the number of the Doppler signal respectively in the volume measurement and in the control volume. For this counting made for each measurement point of the particle velocity, two thresholds are fixed, one on the amplitude of the Doppler signal and the other on the integral of the power spectral

'2 2

**2.2.2 Measurement method of the local concentration profile**

vertical diameter of the test section (Fig. 4).

volume Npt , (-..-) test section.

density. The total number of particles Npt is given by:

n

(5)

f G(f )

n

G(f )

G(f ) = P (f ) <sup>k</sup> and k = 1, 2, 3,...........,N. Considering that the enlargement of the

1 2 f = [ (f - f ) G(f ) / G(f )] (6)

$$\mathbf{N}\_{\mathbf{P}^\mathrm{t}} = \sum\_{\mathbf{i}=1}^{n} (\mathbf{N}\_{\mathbf{P}})\_{\mathbf{i}} \tag{7}$$

with n the number of the measurement point. The local concentration profile is obtained by the plot of the variation of the ratio Np / Npt versus the depth of the measurement volume along the vertical diameter of the test section (Fig. 4).

Fig. 5. a) Validation of the method and calibration of the ultrasonic transducer: 1 glass tank of calibration, 2 lateral wall of the tank, 3 ultrasonic transducer, 4 micrometric displacement system of the transducer, 5 plastic disc, 6 Abrasive cloth band or cylindrical metal rods, 7 ultrasonic Doppler velocimeter, 8 digital storage oscilloscope, 9 Data processor (Plurimat S); b) Validation curve of the signal processing method; c) Calibration curve of the ultrasonic transducer

### **2.2.3 Validation of the processing signal method and calibration of the ultrasonic transducer**

The validation of the method applied for the signal processing consists of a comparison between the results obtained by the data processor (9) and those of the processing signal system integrated into the medical apparatus (7). For this validation we developed a device illustrated in Fig. 5a, it consists of the plastic disc (5) of 160 mm diameter turning with a variable speed motor, and on which a abrasive cloth band (6) is stuck (in Figure 5a, only the

Application of Pulsed Ultrasonic Doppler Velocimetry to

volumetric concentration of the starch is CV = 0.3%.

**3.2.1 Effect of the mean flow velocity**

= 2 m/s.

heterogeneous regime.

**3.2 Velocity and concentration profiles of large particles**

represented by the model of Pai.

the Simultaneous Measurement of Velocity and Concentration Profiles in Two Phase Flow 141

suspension is negligible. In the following results the velocity profile of water alone will be

Fig. 6. Velocity and concentration profiles of water-starch suspension, Re= 42000, the

the results corresponding to the particles of diameter 0.13 and 0.4 mm are presented.

Large particles of high density compared to the carrier fluid, i.e., those where the diameter exceeds the wavelength of the ultrasonic wave, do not follow the flow. In this paper, only

A mean flow velocity range of 1 m/s to 2.5 m/s was used. This range corresponds to the heterogeneous and saltation flow regimes. Figure 7 show the influence of the mean flow velocity on the velocity and the concentration profiles of the solid particles of diameter 0.13 and 0.4 mm respectively. The velocity profiles are parabolas with a top around the pipe axis, very near for dp= 0.13 mm and below for dp= 0.4 mm. For the other particle diameter of 0.27 mm and 0.7 mm (which are not presented in this paper), the tops are below the pipe axis. The presence of the particles near the top wall was observed only for dp = 0.13 mm and Umoy

The concentration profiles are in a better agreement with the observations of the flow made during the experimental tests. Indeed, for a constant volumetric concentration and a mean flow velocity ranging between 1 and 2 m/s, the flow of the particles suspension of diameter 0.27 mm, 0.4 mm and 0.7 mm is a saltation regime. It becomes heterogeneous when the flow mean velocity exceeds 2 m/s. For the particles of diameter 0.13 mm, the flow suspension is

cylindrical metal rods used for the calibration of the ultrasonic transducer are represented). The fine emery grains act as the centers of diffraction moving with a known tangential velocity in the volume measurement. This intersection between the emery grains and the volume measurement is obtained by a micrometric displacement system of the ultrasonic transducer (4) fixed on one of the lateral walls of the tank calibration (2). The Doppler frequency is determined by the acquisition and processing system (9). Figure 5b shows that, in a large tension range, the results obtained from the signal processing of the data processor have a better linearity than those from the signal processing system integrated into the medical apparatus.

For the calibration of the ultrasonic transducer (3), which consists of determining the exact value of the inclination angle of the ultrasonic transducer, the same device as that of the validation of the signal processing method was used, except for the plastic disc where the abrasive cloth band is replaced by cylindrical metal rods (6) of 1 mm diameter and 15 mm length. Figure 5c shows a better linearity between a known tangential velocity Ut of the rods crossing the measurement volume and the value of Ucos determined from the signal processing. The inclination angle of the ultrasonic transducer (*=* 67.4°) determined from the calibration curve is very close to that used in the medical apparatus (*= 67°*).

## **3. Experimental results**

#### **3.1 Velocity and concentration profiles of fine particles**

The rheological study of the starch suspension in water made in a rotating viscometer of coaxial cylinders (Haake RV12), showed that the suspension have a shear thickening behaviour described by the power law rheological model.

$$
\pi = \mathbb{k} \text{ } \varepsilon^n \text{ } \tag{8}
$$

where is the shear stress, k is the flow consistency index and n is the flow behaviour index. These two rheological parameters determined from the flow curves, k = 0.33x10-3 kg/ms and n = 1.1, are necessary to determine the velocity profile using the model of Pai (Brodkey, Lee, Chase (1961) and Brodkey (1963)) valid for the Newtonian and non-Newtonian fluids when the Reynolds number Re is lower than 105. This model is given by:

$$\frac{\mathbf{U(r)}}{\mathbf{U\_{max}}} = \mathbf{1} + \mathbf{a}\_1 \left(\frac{\mathbf{r}}{\mathbf{R}}\right)^{\frac{\mathbf{n}+1}{\mathbf{n}}} + \mathbf{a}\_2 \left(\frac{\mathbf{r}}{\mathbf{R}}\right)^{2\mathbf{m}} \tag{9}$$

where Umax is the maximum velocity generally taken on the pipe axis, R the pipe radius, and r = R - y the variable pipe radius (y is the wall normal distance). The constants a1, a2 and m depend on the nature of the fluid, the boundary conditions and the flow mean velocity. Figure 6 shows the velocity and the concentration profiles of the water-starch suspension obtained along the test section diameter. The velocity profile coincides well with the theoretical profile of Pai, and the concentration profile has a uniform distribution.

According to Furuta et al. (1977) we can thus assume that fine particle suspension which represents a tracer behaves as a homogeneous fluid and the slip velocity of the solid - liquid suspension is negligible. In the following results the velocity profile of water alone will be represented by the model of Pai.

Fig. 6. Velocity and concentration profiles of water-starch suspension, Re= 42000, the volumetric concentration of the starch is CV = 0.3%.

## **3.2 Velocity and concentration profiles of large particles**

Large particles of high density compared to the carrier fluid, i.e., those where the diameter exceeds the wavelength of the ultrasonic wave, do not follow the flow. In this paper, only the results corresponding to the particles of diameter 0.13 and 0.4 mm are presented.

## **3.2.1 Effect of the mean flow velocity**

140 Ultrasonic Waves

cylindrical metal rods used for the calibration of the ultrasonic transducer are represented). The fine emery grains act as the centers of diffraction moving with a known tangential velocity in the volume measurement. This intersection between the emery grains and the volume measurement is obtained by a micrometric displacement system of the ultrasonic transducer (4) fixed on one of the lateral walls of the tank calibration (2). The Doppler frequency is determined by the acquisition and processing system (9). Figure 5b shows that, in a large tension range, the results obtained from the signal processing of the data processor have a better linearity than those from the signal processing system integrated into the

For the calibration of the ultrasonic transducer (3), which consists of determining the exact value of the inclination angle of the ultrasonic transducer, the same device as that of the validation of the signal processing method was used, except for the plastic disc where the abrasive cloth band is replaced by cylindrical metal rods (6) of 1 mm diameter and 15 mm length. Figure 5c shows a better linearity between a known tangential velocity Ut of the rods crossing the measurement volume and the value of Ucos determined from the signal processing. The inclination angle of the ultrasonic transducer (*=* 67.4°) determined from the

The rheological study of the starch suspension in water made in a rotating viscometer of coaxial cylinders (Haake RV12), showed that the suspension have a shear thickening

where is the shear stress, k is the flow consistency index and n is the flow behaviour index. These two rheological parameters determined from the flow curves, k = 0.33x10-3 kg/ms and n = 1.1, are necessary to determine the velocity profile using the model of Pai (Brodkey, Lee, Chase (1961) and Brodkey (1963)) valid for the Newtonian and non-Newtonian fluids

1 2

where Umax is the maximum velocity generally taken on the pipe axis, R the pipe radius, and r = R - y the variable pipe radius (y is the wall normal distance). The constants a1, a2 and m depend on the nature of the fluid, the boundary conditions and the flow mean velocity. Figure 6 shows the velocity and the concentration profiles of the water-starch suspension obtained along the test section diameter. The velocity profile coincides well with the

According to Furuta et al. (1977) we can thus assume that fine particle suspension which represents a tracer behaves as a homogeneous fluid and the slip velocity of the solid - liquid

U(r) r <sup>r</sup> =1+a +a U RR

theoretical profile of Pai, and the concentration profile has a uniform distribution.

n+1 2m <sup>n</sup>

<sup>n</sup> = k (8)

(9)

calibration curve is very close to that used in the medical apparatus (*= 67°*).

when the Reynolds number Re is lower than 105. This model is given by:

max

**3.1 Velocity and concentration profiles of fine particles**

behaviour described by the power law rheological model.

medical apparatus.

**3. Experimental results**

A mean flow velocity range of 1 m/s to 2.5 m/s was used. This range corresponds to the heterogeneous and saltation flow regimes. Figure 7 show the influence of the mean flow velocity on the velocity and the concentration profiles of the solid particles of diameter 0.13 and 0.4 mm respectively. The velocity profiles are parabolas with a top around the pipe axis, very near for dp= 0.13 mm and below for dp= 0.4 mm. For the other particle diameter of 0.27 mm and 0.7 mm (which are not presented in this paper), the tops are below the pipe axis. The presence of the particles near the top wall was observed only for dp = 0.13 mm and Umoy = 2 m/s.

The concentration profiles are in a better agreement with the observations of the flow made during the experimental tests. Indeed, for a constant volumetric concentration and a mean flow velocity ranging between 1 and 2 m/s, the flow of the particles suspension of diameter 0.27 mm, 0.4 mm and 0.7 mm is a saltation regime. It becomes heterogeneous when the flow mean velocity exceeds 2 m/s. For the particles of diameter 0.13 mm, the flow suspension is heterogeneous regime.

Application of Pulsed Ultrasonic Doppler Velocimetry to

profiles tend to that of the carrying fluid.

profiles for Cv= 1%, Re = 44600.

**4. Conclusion**

**3.2.3 Effect of diameter**

the Simultaneous Measurement of Velocity and Concentration Profiles in Two Phase Flow 143

The figure 9a shows that for all the particle diameters used, the velocity profiles of the solid particles have the same trend as that of the carrying fluid. The difference between the velocity profile of the continuous phase and that of the solid phase confirms the existence of the solid-liquid slip velocity which, increases with increasing particle diameter. Figure. 9b shows that for the solid particles of diameter 0.13 mm and 0.27 mm, the local concentration

(a) (b)

Fig. 9. Influence of the particle diameter on: a) the velocity profiles; b) the concentration

The maximum of local concentration profile appears for dp= 0.4 mm and dp = 0.7 mm. The solid particles are present near the pipe top wall only for the small diameter (0.13 mm).

In this experimental chapter, we have tested a new approach measurement in order to determine simultaneously the velocity profiles and the concentration profiles of the solid

Fig. 7. Velocity and concentration profiles of glass bead for Cv= 1%: a) dp= 0.13 mm; b) dp= 0.40 mm

#### **3.2.2 Effect of volumetric concentration**

Figure 8 shows the influence of the volumetric concentration of the solid particles on the velocity and local concentration profiles. Note that the difference between the velocity profile of the solid particles and that of the carrying fluid (Fig. 8a), which represents the solid-liquid slip velocity, increases with the increase in the volumetric concentration. The local concentration profiles (Fig. 8b) present a maximum value, whose position moves away from the internal pipe bottom wall when the volumetric concentration decreases. For the lower volumetric concentration, the local concentration profile tends to that of the carrying fluid (or the fine particles) which is almost uniform. The presence of the particles near the pipe top wall was observed for the volumetric concentration lower than 0.5 %.

Fig. 8. Effect of the particle volumetric concentration on: a) the velocity profiles; b) the local concentration profiles for dp*=* 0.27 mm and Re= 44600.

## **3.2.3 Effect of diameter**

142 Ultrasonic Waves

(a) (b) Fig. 7. Velocity and concentration profiles of glass bead for Cv= 1%: a) dp= 0.13 mm; b) dp=

Figure 8 shows the influence of the volumetric concentration of the solid particles on the velocity and local concentration profiles. Note that the difference between the velocity profile of the solid particles and that of the carrying fluid (Fig. 8a), which represents the solid-liquid slip velocity, increases with the increase in the volumetric concentration. The local concentration profiles (Fig. 8b) present a maximum value, whose position moves away from the internal pipe bottom wall when the volumetric concentration decreases. For the lower volumetric concentration, the local concentration profile tends to that of the carrying fluid (or the fine particles) which is almost uniform. The presence of the particles near the

(a) (b) Fig. 8. Effect of the particle volumetric concentration on: a) the velocity profiles; b) the local

concentration profiles for dp*=* 0.27 mm and Re= 44600.

pipe top wall was observed for the volumetric concentration lower than 0.5 %.

0.40 mm

**3.2.2 Effect of volumetric concentration**

The figure 9a shows that for all the particle diameters used, the velocity profiles of the solid particles have the same trend as that of the carrying fluid. The difference between the velocity profile of the continuous phase and that of the solid phase confirms the existence of the solid-liquid slip velocity which, increases with increasing particle diameter. Figure. 9b shows that for the solid particles of diameter 0.13 mm and 0.27 mm, the local concentration profiles tend to that of the carrying fluid.

Fig. 9. Influence of the particle diameter on: a) the velocity profiles; b) the concentration profiles for Cv= 1%, Re = 44600.

The maximum of local concentration profile appears for dp= 0.4 mm and dp = 0.7 mm. The solid particles are present near the pipe top wall only for the small diameter (0.13 mm).

## **4. Conclusion**

In this experimental chapter, we have tested a new approach measurement in order to determine simultaneously the velocity profiles and the concentration profiles of the solid

Application of Pulsed Ultrasonic Doppler Velocimetry to

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Kikura, H., Yamanaka, G., Aritomi, M. (2004). Effect of Measurement Volume Size on

Lei, K., Taniguchi, N., Kobayashi, T. (2000). LES of Particle-Laden Turbulent Channel Flow Considering SGS Coupling, *Trans JSME B*, Vol.66, No. 651, pp. 2807–2814. Michaelides, E.E., Stock, D.E. (1989). *Turbulence Modification in Dispersed Multiphase Flows*,

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particles (glass bead) and the continuous phase (water) of two phase flow in horizontal pipe. The distinction between the Doppler signals coming from the solid phase and the continuous phase was obtained by imposing a threshold on the integral of the power spectral density. The use of this approach measurement is limited to small concentrations lower than 2%. Indeed when a concentration of 2% is exceeded, the ultrasonic signal is attenuated. This approach measurement shows the effects of the particle diameter and volumetric concentration on the local mean velocity and local mean concentration profiles of the suspensions.

The results obtained show that for the fine particles, the suspension behaves like a homogeneous fluid; the velocity profile is in a better agreement with the Pai's model and the concentration profile is almost uniform. For the large particles, saltation and heterogeneous flow regimes were obtained. These two regimes depend on the diameter and volumetric concentration of the particle, and on the flow mean velocity. The slip velocity which is responsible for the fluid-particle interaction depends on the flow regime.

In our next chapter concerning the solid liquid suspension, PUDV and Particle–Tracking Velocimetry (PTV) will be applied together. The most advantage of PTV is the possibility of measurements of large particles, by which the fluid–particle interactions and the particle– response property will be able to be examined. This allows us perhaps the best understanding of the phenomenon caused by the fluid–particle interactions, and also probably by the particle–particle interactions because of high concentration near the wall. It is also necessary to investigate interactions between these phenomenon and particle motion due to two-way and four-way couplings in a wide range of particle diameter, specific density, and sediment concentration, and then to develop reasonable computer simulation models of two phase horizontal pipe flow.

## **5. Acknowledgment**

This work has been supported by Research Laboratory of Industrial Technologies, University Ibn Khaldoun of Tiaret. The first author would like to thank Professor S. Hadj Ziane, Institute of Physics, University Ibn Khaldoun of Tiaret, for useful discussions as well as for providing support to perform this work.

## **6. References**

particles (glass bead) and the continuous phase (water) of two phase flow in horizontal pipe. The distinction between the Doppler signals coming from the solid phase and the continuous phase was obtained by imposing a threshold on the integral of the power spectral density. The use of this approach measurement is limited to small concentrations lower than 2%. Indeed when a concentration of 2% is exceeded, the ultrasonic signal is attenuated. This approach measurement shows the effects of the particle diameter and volumetric concentration on the local mean velocity and local mean concentration profiles of

The results obtained show that for the fine particles, the suspension behaves like a homogeneous fluid; the velocity profile is in a better agreement with the Pai's model and the concentration profile is almost uniform. For the large particles, saltation and heterogeneous flow regimes were obtained. These two regimes depend on the diameter and volumetric concentration of the particle, and on the flow mean velocity. The slip velocity which is

In our next chapter concerning the solid liquid suspension, PUDV and Particle–Tracking Velocimetry (PTV) will be applied together. The most advantage of PTV is the possibility of measurements of large particles, by which the fluid–particle interactions and the particle– response property will be able to be examined. This allows us perhaps the best understanding of the phenomenon caused by the fluid–particle interactions, and also probably by the particle–particle interactions because of high concentration near the wall. It is also necessary to investigate interactions between these phenomenon and particle motion due to two-way and four-way couplings in a wide range of particle diameter, specific density, and sediment concentration, and then to develop reasonable computer simulation

This work has been supported by Research Laboratory of Industrial Technologies, University Ibn Khaldoun of Tiaret. The first author would like to thank Professor S. Hadj Ziane, Institute of Physics, University Ibn Khaldoun of Tiaret, for useful discussions as well

Alfonsi, G.,Brambilla, S., Chiuch, D. (2003). The Use of an Ultrasonic Doppler Velocimeter in

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Brito, D., Nataf, H.C., Cardin, P., Aubert, J., Masson, J.P. (2001). Ultrasonic Doppler Velocimtry in Liquid Gallium, *Experiments in Fluids*, Vol.31, No. 6, pp. 653-663. Brodkey, R.S., Lee, J., Chasse, R.C. (1961). A Generalized Velocity Distribution for Non-

of Bubbly Flow Using Ultrasonic Velocity Profile Monitor and Video Data

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responsible for the fluid-particle interaction depends on the flow regime.

models of two phase horizontal pipe flow.

as for providing support to perform this work.

**5. Acknowledgment**

**6. References**

the suspensions.

**1. Introduction**

132dB (re 1

between various propulsion technologies in Table 1.

**8**

**Ultrasonic Thruster**

*United States of America*

Alfred C. H. Tan and Franz S. Hover *Massachusetts Institute of Technology*

Acoustic streaming refers to the bulk net flow of fluid generated as a result of intense, freefield ultrasound. This phenomenon, also known as 'quartz wind' or 'sonic wind', is induced by a loss in mean momentum flux due to sound absorption in the fluid medium, leading to a net flow along the transducer axial direction. The transmission of intense sound energy into the fluid is also associated with a resultant force acting on the transducer surface. This resultant "backthrust" can be exploited in underwater vehicles for propulsion or maneuvering purposes. We refer to the device as ultrasonic thruster (UST), shown in Fig. 1, and define it as an ultrasonic transducer made from piezoelectric material, excited by an alternating high-voltage source in the megahertz. We provide a general comparison

Fig. 1. An ultrasonic thrusters (UST) directing a jet through the free water surface.

Jet

The UST we describe is being considered as an alternative small-scale propulsor for underwater robotic devices and systems, because it has no moving parts beyond its membrane and can be mounted flushed with the body of the watercraft. At a sound level of

biofouling and could perform self-cleaning under prolonged water submersion. These novelties in low maintenance and design robustness, coupled with low cost commercially off-the-shelf (COTS) transducers, are attributes which are not found in rotary or biomimetic propulsors of today. For a small transducer diameter of 1cm, thrust generated is in the order of tens of milli-newtons (mN), suitable for systems operating at low Reynolds numbers.

Pa) (Panchal, Takahashi, & Avery, 1995; Tan & Tanaka, 2006), it is destructive to

UltraSonic Thruster (UST)

## **Ultrasonic Thruster**

Alfred C. H. Tan and Franz S. Hover *Massachusetts Institute of Technology United States of America*

## **1. Introduction**

146 Ultrasonic Waves

Varaksin, A;Y., Zaichik, L.I. (2000). Effect of Particles on the Carrier Flow Turbulence,

Xu, H. (2003). *Measurement of Fiber Suspension Flow and Forming Jet Velocity Profile by Pulsed*

*Ultrasonic Doppler Velocimetry*, Ph.D. Thesis, Atlanta, Institute of Paper Science and

*Thermophys. Aeromech*., Vol.7, pp. 237-248.

Technology.

Acoustic streaming refers to the bulk net flow of fluid generated as a result of intense, freefield ultrasound. This phenomenon, also known as 'quartz wind' or 'sonic wind', is induced by a loss in mean momentum flux due to sound absorption in the fluid medium, leading to a net flow along the transducer axial direction. The transmission of intense sound energy into the fluid is also associated with a resultant force acting on the transducer surface. This resultant "backthrust" can be exploited in underwater vehicles for propulsion or maneuvering purposes. We refer to the device as ultrasonic thruster (UST), shown in Fig. 1, and define it as an ultrasonic transducer made from piezoelectric material, excited by an alternating high-voltage source in the megahertz. We provide a general comparison between various propulsion technologies in Table 1.

Fig. 1. An ultrasonic thrusters (UST) directing a jet through the free water surface.

The UST we describe is being considered as an alternative small-scale propulsor for underwater robotic devices and systems, because it has no moving parts beyond its membrane and can be mounted flushed with the body of the watercraft. At a sound level of 132dB (re 1Pa) (Panchal, Takahashi, & Avery, 1995; Tan & Tanaka, 2006), it is destructive to biofouling and could perform self-cleaning under prolonged water submersion. These novelties in low maintenance and design robustness, coupled with low cost commercially off-the-shelf (COTS) transducers, are attributes which are not found in rotary or biomimetic propulsors of today. For a small transducer diameter of 1cm, thrust generated is in the order of tens of milli-newtons (mN), suitable for systems operating at low Reynolds numbers.

Ultrasonic Thruster 149

works on thrust by ultrasonic means can be found in (Allison, Springer, & Van Dam, 2008; Nobunaga, 2004; Wang et al., 2011; Yu & Kim, 2004); we review and expand upon these. We have also made a comparison among these UST technologies, and provide some insights

The UST is made from a membrane actuator mounted in a specially designed waterproof housing, excited by an electrical source at ultrasonic frequency; the UST is generally applied underwater to generate thrust. For this work, the actuator is made of a thin, circular piezoelectric plate. We establish some fundamental concepts of the UST physics leading to thrust as experienced on the transducer surface, and its resulting jet of acoustic streaming into the farfield. Several nomenclatures are defined and used to describe the experimental

As described in the introduction, there are some prior works on the UST found in the literature. The experimental model used in those examples varies in shapes and sizes, and in the following, we provide a basis of comparison among them in terms of thrust density and electrical power density between each UST design. As an introduction, we refer to the mathematical treatment of thrust and acoustic power generation in Eqs. (1) to (4) as originally proposed by (Allison, et al., 2008), and relates thrust to the transducer voltage

Fig. 2. An elemental control volume in the far-field; the elevation angle, azimuth angle and

In Fig. 2, several variables for the transducer and the acoustic field are introduced. The acoustic energy transmits to the right semi-hemisphere, propagating perpendicularly

, and *s* respectively.

*ds*

sin *s d*

> *s d*

. According to (Allison, et al., 2008), thrust experienced on the surface of

*x*

*x'*

of a control volume

,

*S*

through an elemental cross-sectional surface area <sup>2</sup> *dS s d d* sin

into some of the design parameters of ultrasonic propulsion.

supplied, *E*, a parameter reported in most UST-related studies.

2*a*

**2. Underwater Ultrasonic Thruster (UST)**

results in the preceding sections.

distance from the center of transducer are

<sup>2</sup> *dS s d d ds* sin

the transducer is expressed as

**2.1 Thrust generation**

Table 1. Broad comparison of propulsor technologies (Carlton, 2007; Sfakiotakis, Lane, & Davies, 1999; Tan & Hover, 2009).

At the same time, large-scale collaborative swarm of small "microrobots" or "pods" systems are also gaining more interest in terms of low cost and practical operation. Small clusters of exploratory underwater vehicles could also acquire true flexibility in formation morphing, and wide spatial/temporal coverage in search-survey work (Trimmer & Jebens, 1989). More importantly, small water submersible is valuable in cluttered or confined environments such as inside a piping network or complex underwater structures (Egeskov, Bech, Bowley, & Aage, 1995). Naval reconnaissance missions could involve the deployment of clusters of expendable (even biodegradable) small underwater robots for hazardous/security missions such as mine-hunting or surveillance mapping (Doty et al., 1998).

In the following sections, we examine the theoretical background of the UST thrust generation, introduce scaled parameters for comparison between various UST devices found in the literature, examine its transit efficiency, identify some thermal anomalies, and discuss some of the UST design considerations. A detailed construction of the UST will be outlined with underlying insights to materials selection and design principles. For practical demonstration, we have also built a small underwater vehicle named *Huygens*, to establish a miniaturized platform for supporting multi-objectives subsea tasks. The main focus will be exclusively on the transducer-only testing (without nozzle appendages) for thrust and wake characterization as these are fundamentals toward understanding the UST technology. Prior

Maneuverability; reduced impact on vessel internal layout; noise isolation

High efficiency; directional stability; robustness against

advance speeds and loadings

Efficient and maneuverable at

High maneuverability at low

Very small size; no moving parts; short-range acoustic

Table 1. Broad comparison of propulsor technologies (Carlton, 2007; Sfakiotakis, Lane, &

At the same time, large-scale collaborative swarm of small "microrobots" or "pods" systems are also gaining more interest in terms of low cost and practical operation. Small clusters of exploratory underwater vehicles could also acquire true flexibility in formation morphing, and wide spatial/temporal coverage in search-survey work (Trimmer & Jebens, 1989). More importantly, small water submersible is valuable in cluttered or confined environments such as inside a piping network or complex underwater structures (Egeskov, Bech, Bowley, & Aage, 1995). Naval reconnaissance missions could involve the deployment of clusters of expendable (even biodegradable) small underwater robots for hazardous/security missions

In the following sections, we examine the theoretical background of the UST thrust generation, introduce scaled parameters for comparison between various UST devices found in the literature, examine its transit efficiency, identify some thermal anomalies, and discuss some of the UST design considerations. A detailed construction of the UST will be outlined with underlying insights to materials selection and design principles. For practical demonstration, we have also built a small underwater vehicle named *Huygens*, to establish a miniaturized platform for supporting multi-objectives subsea tasks. The main focus will be exclusively on the transducer-only testing (without nozzle appendages) for thrust and wake characterization as these are fundamentals toward understanding the UST technology. Prior

communication

such as mine-hunting or surveillance mapping (Doty et al., 1998).

many speeds; quiet Complex physical design

speeds; quiet Complex physical design

supply

suitable for shallow water

Cycloidal propeller Low-speed maneuverability Complex mechanical

Load- and speed-dependent

High bearing loads; costly

May be inefficient at off design conditions

Complex actuation system

Poor performance at low speeds; vulnerable to ingested debris

structure and maintenance

Poor propulsive efficiency; requires a high-voltage

and maintenance

performance

and complex

Propulsors Advantages Disadvantages

Fixed-pitch propeller Very mature technology; cost

Controllable-pitch propeller High efficiency at different

Waterjet Efficient at high vessel speeds;

Podded drive

Ducted propeller

Biomimetic – body/caudal fin (BCF) locomotion

Davies, 1999; Tan & Hover, 2009).

Biomimetic – Median and/or paired fin (MPF)

Ultrasonic thruster

locomotion

(this work)

effective

line fouling

works on thrust by ultrasonic means can be found in (Allison, Springer, & Van Dam, 2008; Nobunaga, 2004; Wang et al., 2011; Yu & Kim, 2004); we review and expand upon these. We have also made a comparison among these UST technologies, and provide some insights into some of the design parameters of ultrasonic propulsion.

## **2. Underwater Ultrasonic Thruster (UST)**

The UST is made from a membrane actuator mounted in a specially designed waterproof housing, excited by an electrical source at ultrasonic frequency; the UST is generally applied underwater to generate thrust. For this work, the actuator is made of a thin, circular piezoelectric plate. We establish some fundamental concepts of the UST physics leading to thrust as experienced on the transducer surface, and its resulting jet of acoustic streaming into the farfield. Several nomenclatures are defined and used to describe the experimental results in the preceding sections.

#### **2.1 Thrust generation**

As described in the introduction, there are some prior works on the UST found in the literature. The experimental model used in those examples varies in shapes and sizes, and in the following, we provide a basis of comparison among them in terms of thrust density and electrical power density between each UST design. As an introduction, we refer to the mathematical treatment of thrust and acoustic power generation in Eqs. (1) to (4) as originally proposed by (Allison, et al., 2008), and relates thrust to the transducer voltage supplied, *E*, a parameter reported in most UST-related studies.

Fig. 2. An elemental control volume in the far-field; the elevation angle, azimuth angle and distance from the center of transducer are , , and *s* respectively.

In Fig. 2, several variables for the transducer and the acoustic field are introduced. The acoustic energy transmits to the right semi-hemisphere, propagating perpendicularly through an elemental cross-sectional surface area <sup>2</sup> *dS s d d* sin of a control volume <sup>2</sup> *dS s d d ds* sin . According to (Allison, et al., 2008), thrust experienced on the surface of the transducer is expressed as

Ultrasonic Thruster 151

fluid particle is less than it entered due to sound absorption. The distribution of energy gradient then moves the particle away from the source resulting in an overall streaming effect. In another words, the loss in momentum flux across a control volume (Fig. 2) leads to a net force in the direction of the acoustic path. This net force in turn generates hydrodynamic flow

0

where *ux* denotes the time-averaged streaming velocity along the *x*-axis, *Fx* is the radiation

 *c*, and

the fluid. Since mass flow is conserved within the control volume, that is, 0 *ux*

2 2

(m2/s),

where *A* and *B* are characteristic coefficients of the fully developed axial velocity profile (*t*

(dB/m) is the absorption coefficient at a particular sound transmission frequency (Rudenko & Soluian, 1977). Accordingly, Lighthill demonstrated that the radiation force can also be

> <sup>2</sup> *ux <sup>F</sup> x*

In this case, it follows from Eq. (7) that *F* is proportional to <sup>2</sup> *ux* and knowing that *F* is also

Next, the total fluid discharge across the lateral section of the flow in Fig. 3 is given by

From (Tan & Hover, 2009) and later in Section 2.3.4, it can be seen that the streaming field across a lateral section can be approximated by a Gaussian distribution of the following

distance and *C* is a constant associated with the standard deviation of the Gaussian distribution. *ux* reveals a vital difference from conventional propeller design and biomimetic actuation – that at *x* = 0, the streaming velocity at the surface of the transducer is zero. This observation is further verified in the experimental results in Section 2.3.4. Hence the total kinetic energy of the velocity field in unit time from *x* = 0 to *x* = *xf*, where *xf* (m) is the focal

(Fig. 4), and the mass flow rate through the elemental disc is 2

, where *ux* (m/s) is the axial velocity in unit time, *r* (m) is the radial

*A u ee B*

*x*

represented by the Reynolds stress along the axial direction:

proportional to <sup>2</sup> *E* , *ux* is seen to scale directly with *E*.

distance from the flat transducer surface, is given by

*<sup>x</sup> <sup>x</sup> x x u p <sup>u</sup> u F x x x*

  2

2

*x Bx*

 = 2

(5)

and using boundary conditions *u u x x* 0 0, 0 ,

(6)

(7)

(kg/m·s) is the dynamic viscosity of

for low intensity sound, and

 *u r dr <sup>r</sup>* .

*x*

, Eq. (5)

in a steady state incompressible medium, as governed by the Navier-Stokes equation,

force along the *x*-axis, *p*0 is defined as 0 0 *p*

is the kinematic viscosity

can be solved by assuming *<sup>x</sup> F Ae <sup>x</sup>*

to obtain

), and

2 *u A u rr r r*

*<sup>C</sup> u ue r x*

form,

$$T = \rho \upsilon\_o^2 a^2 \,\pi \int\_0^{\theta\_1} \frac{J\_1(ka\sin\theta)^2}{\sin\theta} d\theta \tag{1}$$

where (kg/m3), *o* (m/s), *a* (m), *k*, , and *J*1() denote the fluid density, transducer surface velocity, radius of the transducer, wavenumber, sound absorption coefficient, and Bessel function of the first kind, respectively, and we consider <sup>1</sup> 1 3.832 sin *ka* (Blackstock, 2000) as the upper limit of the dominant ultrasonic beamwidth.

The relationship between the acoustic power along the transducer axial direction x and the ultrasonic thrust is given by a simple relationship (Allison, et al., 2008)

$$P\_{\mathfrak{x}} = {}^{c}\!\!\!\!\!\!\!\!/ \mathfrak{y}\tag{2}$$

where *c* (m/s) denotes the sound speed, and relates to the efficiency which will be elaborated in the next paragraph. As we verify below, this also means the thrust is considerably lower than would a rotary propulsor operating at the same power level.

At *s* = 0, this acoustic power radiation is associated with the electrical power consumption across the transducer. The electrical power would provide an approximation to the acoustic power loading, which relates to the thrust force, and is reflected in the following considerations through an efficiency constant, ; (i) electrical power lost across the transducer is not wholly transferred into the medium; (ii) acoustic loading at the sharp dominant resonant frequency of the transducer may not be precisely tuned; (iii) it is difficult to consider the equivalent acoustic load in the lumped circuit impedance; (iv) although the acoustic power is mainly generated within the narrow ultrasonic beam, some losses also occur outside the beamwidth.

By relating the thrust production to the root mean square of the transducer voltage supplied, *Erms*, it can be equated as

$$T = \frac{\eta E\_{rms}^2}{c \operatorname{Re}(\Re)}\tag{3}$$

where Re() is the real component of the transducer impedance, and the electrical power,

$$P = \frac{E\_{rms}^2}{\text{Re}(\Re)}\tag{4}$$

corresponds to *Px* at *s* = 0. This thrust scaling with squared voltage in (3) will be used in Section 2.3.4.

#### **2.2 Acoustic streaming**

Following Lighthill (Lighthill, 1978), acoustic streaming arises because of acoustic energy absorption along the path of propagation in a viscous, dissipative fluid medium. A simple explanation of the mechanism can be thought of as exit momentum flux from each exposed

2 2 1 0

where

(kg/m3),

*o* (m/s), *a* (m), *k*,

the upper limit of the dominant ultrasonic beamwidth.

where *c* (m/s) denotes the sound speed, and

considerations through an efficiency constant,

occur outside the beamwidth.

Section 2.3.4.

**2.2 Acoustic streaming**

supplied, *Erms*, it can be equated as

function of the first kind, respectively, and we consider <sup>1</sup>

ultrasonic thrust is given by a simple relationship (Allison, et al., 2008)

sin *<sup>o</sup> J ka T a <sup>d</sup>*

velocity, radius of the transducer, wavenumber, sound absorption coefficient, and Bessel

The relationship between the acoustic power along the transducer axial direction x and the

*xP cT*

elaborated in the next paragraph. As we verify below, this also means the thrust is

At *s* = 0, this acoustic power radiation is associated with the electrical power consumption across the transducer. The electrical power would provide an approximation to the acoustic power loading, which relates to the thrust force, and is reflected in the following

transducer is not wholly transferred into the medium; (ii) acoustic loading at the sharp dominant resonant frequency of the transducer may not be precisely tuned; (iii) it is difficult to consider the equivalent acoustic load in the lumped circuit impedance; (iv) although the acoustic power is mainly generated within the narrow ultrasonic beam, some losses also

By relating the thrust production to the root mean square of the transducer voltage

where Re() is the real component of the transducer impedance, and the electrical power,

 2 Re *Erms <sup>T</sup> c*

> 2 Re

corresponds to *Px* at *s* = 0. This thrust scaling with squared voltage in (3) will be used in

Following Lighthill (Lighthill, 1978), acoustic streaming arises because of acoustic energy absorption along the path of propagation in a viscous, dissipative fluid medium. A simple explanation of the mechanism can be thought of as exit momentum flux from each exposed

considerably lower than would a rotary propulsor operating at the same power level.

<sup>1</sup> <sup>2</sup>

sin

1

(1)

, and *J*1() denote the fluid density, transducer surface

3.832 sin *ka*

(2)

relates to the efficiency which will be

; (i) electrical power lost across the

(3)

*Erms <sup>P</sup>* (4)

(Blackstock, 2000) as

fluid particle is less than it entered due to sound absorption. The distribution of energy gradient then moves the particle away from the source resulting in an overall streaming effect. In another words, the loss in momentum flux across a control volume (Fig. 2) leads to a net force in the direction of the acoustic path. This net force in turn generates hydrodynamic flow in a steady state incompressible medium, as governed by the Navier-Stokes equation,

$$
\rho \,\overline{u}\_{\mathbf{x}} \frac{\partial \overline{u}\_{\mathbf{x}}}{\partial \mathbf{x}} = -\frac{\partial \overline{p}\_0}{\partial \mathbf{x}} + \mu \frac{\partial^2 \overline{u}\_{\mathbf{x}}}{\partial \mathbf{x}^2} + F\_{\mathbf{x}} \tag{5}
$$

where *ux* denotes the time-averaged streaming velocity along the *x*-axis, *Fx* is the radiation force along the *x*-axis, *p*0 is defined as 0 0 *p c* , and (kg/m·s) is the dynamic viscosity of the fluid. Since mass flow is conserved within the control volume, that is, 0 *ux x* , Eq. (5) can be solved by assuming *<sup>x</sup> F Ae <sup>x</sup>* and using boundary conditions *u u x x* 0 0, 0 , to obtain

$$\overline{\mu}\_x = \frac{A}{\nu \left(\mathcal{B}^2 - \mathcal{B}^2\right)} \left[e^{-\mathcal{B}^\chi x} - e^{-\mathcal{B}^\chi x}\right] \tag{6}$$

where *A* and *B* are characteristic coefficients of the fully developed axial velocity profile (*t* ), and is the kinematic viscosity (m2/s), = 2 for low intensity sound, and (dB/m) is the absorption coefficient at a particular sound transmission frequency (Rudenko & Soluian, 1977). Accordingly, Lighthill demonstrated that the radiation force can also be represented by the Reynolds stress along the axial direction:

$$\overline{F}' = -\frac{\partial \,\rho \,\overline{u}\_x^2}{\partial x} \tag{7}$$

In this case, it follows from Eq. (7) that *F* is proportional to <sup>2</sup> *ux* and knowing that *F* is also proportional to <sup>2</sup> *E* , *ux* is seen to scale directly with *E*.

Next, the total fluid discharge across the lateral section of the flow in Fig. 3 is given by 2 *u A u rr r r* (Fig. 4), and the mass flow rate through the elemental disc is 2 *u r dr <sup>r</sup>* . From (Tan & Hover, 2009) and later in Section 2.3.4, it can be seen that the streaming field across a lateral section can be approximated by a Gaussian distribution of the following form, 2 <sup>2</sup> 2 *r <sup>C</sup> u ue r x* , where *ux* (m/s) is the axial velocity in unit time, *r* (m) is the radial distance and *C* is a constant associated with the standard deviation of the Gaussian distribution. *ux* reveals a vital difference from conventional propeller design and biomimetic actuation – that at *x* = 0, the streaming velocity at the surface of the transducer is zero. This observation is further verified in the experimental results in Section 2.3.4. Hence the total kinetic energy of the velocity field in unit time from *x* = 0 to *x* = *xf*, where *xf* (m) is the focal distance from the flat transducer surface, is given by

Ultrasonic Thruster 153

1 111 <sup>1</sup>

While Eq. (9) sums up the total kinetic energy within the streaming field up to the focal distance, streaming at distances above *xf* will evidently slow down, and free turbulence occurs due to the boundary between the stationary ambient water and the insonified flow – a process called entrainment. We consider regime *x* > *xf* to be no longer reliable or valid for *K.E.* calculation. Eq. (9) will be used in Section 2.3.4. Finally, it follows earlier that *ux* scales directly with *E* and knowing that *K.E.* is also proportional to <sup>2</sup> *ux* from Eq. (8), *K.E.* is seen to scale directly with *E*2. This scaling of *K.E.* with square voltage will be used in Section 2.3.4 to

*B B B*

determine the streaming energy and a comparison is made across other UST devices.

In this section, we characterize thrust and wake energy for a specific UST design, and then investigate and how these properties can be modified using various source voltages. An underwater vehicle prototype was also constructed to demonstrate the ultrasonic

We use standard piezoelectric transducer technology for the conversion of electrical to acoustical energy. The transducer (Murata Manufacturing Co. Ltd) is made from a circular PZT plate measuring 7mm in diameter, housed in a 10mm diameter waterproof metallic

> PZT Metal casing UST Thin wire

Plastic base Potting material Lead terminal

> Connected to power amplifier

Fig. 5. Construction of the UST (adapted from Murata Manufacturing Co. Ltd).

In our prototype vehicle described below, three USTs are connected to switches for actuation control, and 50 coaxial cables connect the three switches to a single power amplifier (ENI 3100L). The ENI unit accepts an oscillatory input up to a maximum of 1Vrms, and amplifies the output voltage by a gain of 50dB for a 50 output impedance. It is a Class A amplifier which means it will be unconditionally stable, and maintains linearity even with a combination of mismatched source and load impedance. When the ultrasonic transducer

Coaxial cable

*B B*

2

<sup>2</sup> <sup>2</sup>

*e e*

*Bx <sup>C</sup>*

*f f*

*x B x*

2 2 (9)

*R*

<sup>2</sup> 22 2

**2.3 Thrust and wake experimental setup**

**2.3.1 UST hardware and methods**

propulsion capability.

casing as shown in Fig. 5.

2 2

1 1 . .

*A C K E <sup>e</sup> <sup>e</sup>*

*f*

$$\begin{aligned} K.E. &= \int\_0^{\chi\_f} \int\_0^R \rho \, u\_x u\_r \, 2\pi \, r \, dr d\mathbf{x} \\ &= 2\pi \rho \int\_0^{\chi\_f} \int\_0^R u\_x^2 \, r \, e^{-\frac{r^2}{2C^2}} dr d\mathbf{x} \end{aligned} \tag{8}$$

Fig. 4. An elemental disc sectioned laterally from the ultrasonic field. Axis of the transducer passes through the center of the concentric circles. The shaded annulus area, 2 *r r* , is an elemental area through which flow discharges.

where *R* (m) is the radius of *ur* (m/s) profile subtended by 1 at *xf*, and the overbar is omitted for simplicity. Substituting Eq. (6) into Eq. (8), and solving the double integral, the total kinetic energy in unit time becomes

*x r*

*<sup>r</sup> x R <sup>C</sup> <sup>x</sup>*

0 0

*x R*

*f*

2

*r*

gradual decline.

. . 2

*K E u u r drdx*

Fig. 3. Velocity distribution of the acoustic streaming. Lateral velocity profile approximates a Gaussian distribution while axial velocity follows a rapid increase in velocity before a

Lateral velocity profile, *ur*

Fig. 4. An elemental disc sectioned laterally from the ultrasonic field. Axis of the transducer

omitted for simplicity. Substituting Eq. (6) into Eq. (8), and solving the double integral, the

passes through the center of the concentric circles. The shaded annulus area, 2

*r*

 *r*

where *R* (m) is the radius of *ur* (m/s) profile subtended by

*R*

elemental area through which flow discharges.

2a

*u*

UST

total kinetic energy in unit time becomes

0 0

*f*

2 2

Axial velocity profile, *ux*

(8)

*x*

*ur|*

*u*

*xf*

 *r r* , is an

*ur*

1 at *xf*, and the overbar is

*u r e drdx*

*xf*

*u*

*r*

2 2

$$\begin{aligned} \text{K.E.} &= \frac{\pi \rho \, A^2 \mathbb{C}^2}{\nu^2 \left(\mathcal{B}^2 - \beta^2\right)^2} \Big( -\frac{1}{\beta} e^{-2\beta x\_f} + \frac{1}{\beta + B} e^{-(\beta + B)x\_f} - \\ &\frac{1}{B} e^{-2\beta x\_f} + \frac{1}{\beta} - \frac{1}{\beta + B} + \frac{1}{B} \right) \times \left( 1 - e^{-\frac{R^2}{2\mathcal{C}^2}} \right) \end{aligned} \tag{9}$$

While Eq. (9) sums up the total kinetic energy within the streaming field up to the focal distance, streaming at distances above *xf* will evidently slow down, and free turbulence occurs due to the boundary between the stationary ambient water and the insonified flow – a process called entrainment. We consider regime *x* > *xf* to be no longer reliable or valid for *K.E.* calculation. Eq. (9) will be used in Section 2.3.4. Finally, it follows earlier that *ux* scales directly with *E* and knowing that *K.E.* is also proportional to <sup>2</sup> *ux* from Eq. (8), *K.E.* is seen to scale directly with *E*2. This scaling of *K.E.* with square voltage will be used in Section 2.3.4 to determine the streaming energy and a comparison is made across other UST devices.

#### **2.3 Thrust and wake experimental setup**

In this section, we characterize thrust and wake energy for a specific UST design, and then investigate and how these properties can be modified using various source voltages. An underwater vehicle prototype was also constructed to demonstrate the ultrasonic propulsion capability.

#### **2.3.1 UST hardware and methods**

We use standard piezoelectric transducer technology for the conversion of electrical to acoustical energy. The transducer (Murata Manufacturing Co. Ltd) is made from a circular PZT plate measuring 7mm in diameter, housed in a 10mm diameter waterproof metallic casing as shown in Fig. 5.

Fig. 5. Construction of the UST (adapted from Murata Manufacturing Co. Ltd).

In our prototype vehicle described below, three USTs are connected to switches for actuation control, and 50 coaxial cables connect the three switches to a single power amplifier (ENI 3100L). The ENI unit accepts an oscillatory input up to a maximum of 1Vrms, and amplifies the output voltage by a gain of 50dB for a 50 output impedance. It is a Class A amplifier which means it will be unconditionally stable, and maintains linearity even with a combination of mismatched source and load impedance. When the ultrasonic transducer

Ultrasonic Thruster 155

20

15

10

Torque (mNm)

5

0

Water

amp. Nd-YLF

Digital PIV camera

Laser sheet

UST

Power

Fig. 7. Calibration of the test rig. Each of the four points shown is an average of four separate

0 9.8 19.6 29.4 39.2 49 Dial gauge force (mN)

A 2-dimensional Digital Particle Image Velocimetry (DPIV) provides an accurate depiction of the UST wake, and beyond the entrainment boundary in the far-field. In similarly-scaled conditions, it has been reported that a 2% standard deviation at the point of maximum velocity can be expected with DPIV (Myers, Hariharan, & Banerjee, 2008). The DPIV system is set up in a water tank measuring 2.4m0.7m0.7m, as shown in Fig. 8. Calculated particle velocities are subject to noise depending predominantly on the interrogation window size, the number of seeded particles, and the sampling rate. We made efforts to tune these for the

(a) (b)

Sync

hronize

image acquisitio

n

d

Camera

UST

Laser sheet

Fig. 8. (a) Schematic diagram of the DPIV tank setup.  (b) A top view

Sheet optics

A pulsed laser sheet, produced by a Quantronix diode pumped Q-switched frequency laser (Darwin-527-30M) and spreads horizontally through the water tank from the outside, coincident with the UST axis. The tank is seeded with 50m polyamide particles, and a camera viewing the laser sheet perpendicularly traces the streaming particles when the UST is operating. The camera samples 300 timed, paired images at 400Hz, in a 0.2m0.2m field of

force applications using a sensitive dial gauge.

**2.3.3 Acoustic streaming measurement**

of the UST wake measurement setup.

lowest noise level.

Signal gen. (B&K 4011A)

emits intense acoustic energy into the fluid, the thin metal housing provides excellent heat dissipation. Natural convection and acoustic streaming also aid in carrying away heat from the transducer surface (Tan & Hover, 2010a).

## **2.3.2 Thrust force measurement**

It is important to develop a reliable underwater thrust measurement method, especially for small thrust magnitudes as is the case of the UST. Most load cells are either non-submersible or could not provide sufficient sensitivity/resolution required at small driving forces. While thrust can also be inferred from acoustic intensity measurement using a hydrophone, it poses some challenges unique to the UST setup, such as membrane cavitation, heating effect, and reading errors averaged from a finite-size hydrophone. Indeed, (Hariharan et al., 2008) reported that acoustic intensity measurements do not perform well, having an error in excess of 20% with experimental data.

In order to accurately measure the thrust produced by the UST, we developed an approach which allows sensitivity control by sliding the UST along an L-shaped arm. Moment is measured with a high precision torque sensor. Other methods have been proposed for measuring these very fine-scale forces, for example, to attach and submerge a UST on one end of a vertical pendulum, hinged off-center, with the other end flexing a strain gauge (Allison, et al., 2008). Another approach is to attach the UST to a free-hanging wire and take photographs of the displacement as the UST is being actuated (Wang, et al., 2011; Yu & Kim, 2004). We found that the setup in Fig. 6 provides very good accuracy and repeatability, as indicated in the calibration plot of Fig. 7. The torque meter accuracy provided by the manufacturer is 0.09mNm, and the absolute error in the calibration thrust force averages about 0.6mN, when our dial gauge is positioned 0.5m from the torque axis on the L-arm.

Fig. 6. (a) The semi-anechoic water tank and torque sensor used to measure UST thrust; thrust is generated in the direction perpendicular to the page. (b) A plan view of the UST thrust measurement setup.

Hence the total force uncertainty is around 0.8mN. Torque calibration is performed prior to all test sets. Thrust stabilizes and is recorded about ten seconds after turning on the power; then the power is turned off. We maintain a minimum of ten-second rest period between all tests, to allow for cooling and for the water to settle. The UST together with the L-shaped arm is submerged in an ultrasound semi-anechoic tank measuring 1.2m0.6m0.6m, filled with distilled water and covered with an acrylic sheet.

emits intense acoustic energy into the fluid, the thin metal housing provides excellent heat dissipation. Natural convection and acoustic streaming also aid in carrying away heat from

It is important to develop a reliable underwater thrust measurement method, especially for small thrust magnitudes as is the case of the UST. Most load cells are either non-submersible or could not provide sufficient sensitivity/resolution required at small driving forces. While thrust can also be inferred from acoustic intensity measurement using a hydrophone, it poses some challenges unique to the UST setup, such as membrane cavitation, heating effect, and reading errors averaged from a finite-size hydrophone. Indeed, (Hariharan et al., 2008) reported that acoustic intensity measurements do not perform well, having an error in

In order to accurately measure the thrust produced by the UST, we developed an approach which allows sensitivity control by sliding the UST along an L-shaped arm. Moment is measured with a high precision torque sensor. Other methods have been proposed for measuring these very fine-scale forces, for example, to attach and submerge a UST on one end of a vertical pendulum, hinged off-center, with the other end flexing a strain gauge (Allison, et al., 2008). Another approach is to attach the UST to a free-hanging wire and take photographs of the displacement as the UST is being actuated (Wang, et al., 2011; Yu & Kim, 2004). We found that the setup in Fig. 6 provides very good accuracy and repeatability, as indicated in the calibration plot of Fig. 7. The torque meter accuracy provided by the manufacturer is 0.09mNm, and the absolute error in the calibration thrust force averages about 0.6mN, when our dial gauge is positioned 0.5m from the torque axis on the L-arm.

(a) (b)

Torque

meter UST

Fig. 6. (a) The semi-anechoic water tank and torque sensor used to measure UST thrust; thrust is generated in the direction perpendicular to the page. (b) A plan view of the UST

Power amp.

Signal generator (B&K 4011A)

Hence the total force uncertainty is around 0.8mN. Torque calibration is performed prior to all test sets. Thrust stabilizes and is recorded about ten seconds after turning on the power; then the power is turned off. We maintain a minimum of ten-second rest period between all tests, to allow for cooling and for the water to settle. The UST together with the L-shaped arm is submerged in an ultrasound semi-anechoic tank measuring 1.2m0.6m0.6m, filled

the transducer surface (Tan & Hover, 2010a).

**2.3.2 Thrust force measurement**

excess of 20% with experimental data.

thrust measurement setup.

Torque display Torque meter

> balance weight

with distilled water and covered with an acrylic sheet.

Acrylic sheet

UST Counter-

90

50 coaxial cable

Water

Ultrasound absorber

Fig. 7. Calibration of the test rig. Each of the four points shown is an average of four separate force applications using a sensitive dial gauge.

#### **2.3.3 Acoustic streaming measurement**

A 2-dimensional Digital Particle Image Velocimetry (DPIV) provides an accurate depiction of the UST wake, and beyond the entrainment boundary in the far-field. In similarly-scaled conditions, it has been reported that a 2% standard deviation at the point of maximum velocity can be expected with DPIV (Myers, Hariharan, & Banerjee, 2008). The DPIV system is set up in a water tank measuring 2.4m0.7m0.7m, as shown in Fig. 8. Calculated particle velocities are subject to noise depending predominantly on the interrogation window size, the number of seeded particles, and the sampling rate. We made efforts to tune these for the lowest noise level.

Fig. 8. (a) Schematic diagram of the DPIV tank setup.  (b) A top view of the UST wake measurement setup.

A pulsed laser sheet, produced by a Quantronix diode pumped Q-switched frequency laser (Darwin-527-30M) and spreads horizontally through the water tank from the outside, coincident with the UST axis. The tank is seeded with 50m polyamide particles, and a camera viewing the laser sheet perpendicularly traces the streaming particles when the UST is operating. The camera samples 300 timed, paired images at 400Hz, in a 0.2m0.2m field of

Ultrasonic Thruster 157

reported in another publication (Tan & Hover, 2010a). The kinetic energy data in Fig. 9(b) show similar trend as well. Using the *K.E.*-*E*2 proportionality relationship from Section 2.2, the scaled kinetic energy at 54Vrms is calculated to be 1.510-7W/V2 respectively. Both scaling of thrust and *K.E.* is important when we compare various UST devices later in Section 2.5.

(a) (b)

50

0

UST

100

150

Axis

distance (mm)

200

20 40 Output voltage (Vrms)

<sup>0</sup> <sup>60</sup>

0 50 Transverse distance (mm)

Scaled

0

80

1

2

3

4 5

6 10- <sup>7</sup>

kinetic energy

(a) (b)

0

3

Kinetic energy

4

5

10- <sup>4</sup>

K.E. Scaled K.E.

2

1

Fig. 11. (a) Measured thrust versus input voltage to the power amplifier using a 7MHz sinusoidal signal. Data appear to saturate above 60Vrms, which implies a disproportionate relationship. (b) Total kinetic energy versus output voltage of the power amplifier using a 7MHz sinusoidal signal. Data appear to saturate above 55Vrms, which also implies a

Although increasing the output voltage always increases thrust, the wake velocity of the sinusoidal source appears to saturate near 55Vrms. The phenomenon of saturation can be

Fig. 10. (a) Digital Particle Image Velocimetry (DPIV) image of a jet at 7MHz, 54Vrms. (b) Processed DPIV velocity field with each velocity contour step at 0.05m/s interval. A focal

0.01

0.008

0.006

0.004

0.002

Scaled t

hrust (mN

/

V2)

0

Streaming velocity (m

/s)

0.2

0.25

0.15

0.1

0.05

point can be clearly seen at (0mm, 120mm).

Thrust Scaled thrust

0 20 40 60 80 Output voltage (Vrms)

Axis

20

15

10

5

T

hrust (mN)

0

distance (mm)

50

0

100

150

200

0 50 Transverse distance (mm)

disproportionate relationship.

view. Post-processing is carried out using DaVis 7.1 software. The UST transducer is positioned at 1.2m from the sheet optics, 0.4m from each adjacent tank wall, and 0.3m below the water surface. The time taken for the stream to become established has been reported variously at about 0.5s (Loh & Lee, 2004) and 20s (Kamakura, Sudo, Matsuda, & Kumamoto, 1996). We allow at least one minute of flow before the camera starts recording. Specific kinetic energy of the flow up to the focal distance *xf* is shown in the next section, which averages 150 measurements; recording the frames takes less than one second. Then the power is turned off, and the tank water is allowed to settle for at least one minute. This schedule is not the same for thrust measurements, as the transducer is powered and cooled for a considerably longer time during DPIV tests. A more detailed analysis of the transducer heating is presented in Section 3.

#### **2.3.4 Thrust and streaming results**

Fig. 9(a) shows thrust force as a function of frequency, for a sinusoidal waveform. The thrust has obvious peaks near 11mN when operated at 7MHz, which can also be computed using the thickness mode frequency constant, *N fh <sup>t</sup>* <sup>0</sup> , where *h* (m) is the thickness of the PZT, and 1970 *Nt* as specified by the manufacturer. We will focus on this frequency in most of the discussion to follow. Fig. 9(b) illustrates the DPIV velocity field for a sinusoidal waveform at 7MHz, with amplified output voltage 54Vrms. From Fig. 10(a) and 10(b), the maximum axial streaming velocity is observed at the point (0mm, 120mm) in the DPIV image, illustrating a fundamental feature of the UST – *that net fluid flow is zero at the transducer face*. Considering the same waveform configurations and frequencies as in Fig. 9(a), a similar peak at 7MHz in the total kinetic energy can be seen in Fig. 9(b).

Fig. 9. (a) Measured thrust versus source frequency for sinusoidal waveforms supplied at 59Vrms. (b) Total kinetic energy versus source frequency, from DPIV. The sinusoidal signal is supplied at 54Vrms.

Figs. 11(a) and 11(b) summarize our findings specifically at the 7MHz resonant point. Thrust generally increases with output voltage, but then starts to flatten out above the amplified output voltage of 60Vrms. From Fig. 12 and from Eq. (3), the corresponding scaled thrust level is 3.810-3mN/V2 at 59Vrms. Scaled thrust decreases gradually as the output voltage increases, and the absolute thrust appears to saturate above 60Vrms; see Fig. 12 – a result also

view. Post-processing is carried out using DaVis 7.1 software. The UST transducer is positioned at 1.2m from the sheet optics, 0.4m from each adjacent tank wall, and 0.3m below the water surface. The time taken for the stream to become established has been reported variously at about 0.5s (Loh & Lee, 2004) and 20s (Kamakura, Sudo, Matsuda, & Kumamoto, 1996). We allow at least one minute of flow before the camera starts recording. Specific kinetic energy of the flow up to the focal distance *xf* is shown in the next section, which averages 150 measurements; recording the frames takes less than one second. Then the power is turned off, and the tank water is allowed to settle for at least one minute. This schedule is not the same for thrust measurements, as the transducer is powered and cooled for a considerably longer time during DPIV tests. A more detailed analysis of the transducer heating is presented in Section 3.

Fig. 9(a) shows thrust force as a function of frequency, for a sinusoidal waveform. The thrust has obvious peaks near 11mN when operated at 7MHz, which can also be computed using the thickness mode frequency constant, *N fh <sup>t</sup>* <sup>0</sup> , where *h* (m) is the thickness of the PZT, and 1970 *Nt* as specified by the manufacturer. We will focus on this frequency in most of the discussion to follow. Fig. 9(b) illustrates the DPIV velocity field for a sinusoidal waveform at 7MHz, with amplified output voltage 54Vrms. From Fig. 10(a) and 10(b), the maximum axial streaming velocity is observed at the point (0mm, 120mm) in the DPIV image, illustrating a fundamental feature of the UST – *that net fluid flow is zero at the transducer face*. Considering the same waveform configurations and frequencies as in Fig.

(a) (b)

4

3

4

10- <sup>4</sup>

2

Kinetic energy

1

0

6 8 10 Frequency (MHz)

Fig. 9. (a) Measured thrust versus source frequency for sinusoidal waveforms supplied at 59Vrms. (b) Total kinetic energy versus source frequency, from DPIV. The sinusoidal signal is

Figs. 11(a) and 11(b) summarize our findings specifically at the 7MHz resonant point. Thrust generally increases with output voltage, but then starts to flatten out above the amplified output voltage of 60Vrms. From Fig. 12 and from Eq. (3), the corresponding scaled thrust level is 3.810-3mN/V2 at 59Vrms. Scaled thrust decreases gradually as the output voltage increases, and the absolute thrust appears to saturate above 60Vrms; see Fig. 12 – a result also

9(a), a similar peak at 7MHz in the total kinetic energy can be seen in Fig. 9(b).

<sup>0</sup> 6 8 <sup>10</sup> Frequency (MHz)

**2.3.4 Thrust and streaming results**

12

6 4 2

8 10

4

T

hrust (mN)

supplied at 54Vrms.

reported in another publication (Tan & Hover, 2010a). The kinetic energy data in Fig. 9(b) show similar trend as well. Using the *K.E.*-*E*2 proportionality relationship from Section 2.2, the scaled kinetic energy at 54Vrms is calculated to be 1.510-7W/V2 respectively. Both scaling of thrust and *K.E.* is important when we compare various UST devices later in Section 2.5.

Fig. 10. (a) Digital Particle Image Velocimetry (DPIV) image of a jet at 7MHz, 54Vrms. (b) Processed DPIV velocity field with each velocity contour step at 0.05m/s interval. A focal point can be clearly seen at (0mm, 120mm).

Fig. 11. (a) Measured thrust versus input voltage to the power amplifier using a 7MHz sinusoidal signal. Data appear to saturate above 60Vrms, which implies a disproportionate relationship. (b) Total kinetic energy versus output voltage of the power amplifier using a 7MHz sinusoidal signal. Data appear to saturate above 55Vrms, which also implies a disproportionate relationship.

Although increasing the output voltage always increases thrust, the wake velocity of the sinusoidal source appears to saturate near 55Vrms. The phenomenon of saturation can be

Ultrasonic Thruster 159

To our knowledge, there are only three experimental works on ultrasonic propulsors reported from (Allison, et al., 2008), (Yu & Kim, 2004), and (Wang, et al., 2011); we compare them with our UST in terms of thrust density, scaled thrust density and power density, in Table 2. As our UST system was operating at a resonance frequency and high voltage, it is difficult to make a fair and direct comparison of performance. We have employed a much higher power level, resulting in a very high thrust level and higher scaled thrust density.

> Allison et al*.* (Allison, et al., 2008)

Frequency (MHz) 5.5 10.8 17.8 7.0 Voltage (V) 24.5 46 140 59 Electrical power (W) 5 -- -- 69.5 Transducer surface area (mm2) /4102 55 /21.282 /472 Thrust (mN) 2.25 5.6 2.3 13.5 Thrust density (N/m2) 28.6 224 893.7 350 Scaled thrust density (N/m2V2) 0.05 0.11 0.04 0.10 Electrical power density (kW/m2) 64 -- -- 1806

This latter property is important in applications because it indicates a very compact force source operating with reasonable voltage levels, exploitable to benefit from many of its

Fig. 13. Thrust force produced by the UST versus driving electrical power. The *l* and *h* subscripts indicate evident low- and high-power regimes. The output voltage to the

50 100 Electrical power (W)

7MHz Sinusoid 7MHz Squarewave

*h,square* =3.9%

<sup>0</sup> <sup>150</sup>

Yu et al*.* (Yu & Kim, 2004)

Z. Wang et al*.* (Wang, et al., 2011)

This work

**2.5 Ultrasonic propulsion design considerations**

Table 2. Performance of different UST devices.

sinusoid is 59Vrms, and for the square wave is 54Vrms.

0

5

T

hrust (mN)

10

*l,sinusoid* =33.6%

15

unique ultrasonic attributes we discussed earlier in the introduction.

*h,sinusoid* =8.9%

*l,square* =17.5%

Properties

explained by distortion in finite-amplitude traveling waves, according to weak shock theory. On the other hand, the fact that thrust in this case increases with input power despite the saturation of velocity highlights an unusual observation – that thrust production mechanism involves the wake only indirectly, and in a manner that is distinct from other propulsors. This fact may offer some interesting avenues for UST design, where the wake and the thrust force could be manipulated independently. This is especially useful in a scenario where larger thrust is desired but the wake has to be weak at the same time, for example, to minimize stirring up particulates near the seabed.

In summary, increasing the output voltage of the power amplifier will no doubt increase the thrust and kinetic energy production of the transducer, but at the same time, introduces an undesirable disproportionate relationship (Tan & Hover, 2010a). This will be further discussed in Section 3.

#### **2.4 Small underwater vehicle,** *Huygens*

We designed and constructed a small, streamlined shell with three embedded UST devices for propulsion and steering in the horizontal plane. The shell measures 215mm160mm80mm, profiled by a truncated NACA 0054 airfoil in the side view, and a truncated NACA 0025 airfoil in the plan view, as shown in Fig. 12(a). The shell is made from high-strength urethane foam for buoyancy, and coated with polyurethane. A UST is positioned at the rear end of the craft to provide forward thrust, and two USTs subtending 120° are symmetrically located on each side of the front end – at the "fish eyes" position. Together, these provide the right/left steering and backing thrust. Inside the shell, two rectangular cavities are machined, measuring 100mm100mm35mm, and 45mm60mm30mm. The shell can be opened into two halves via a stepped mid-section opening, lined with double O-rings for a watertight seal. The cylindrical UST seats are also lined with O-rings. The vent shown in the top left corner of Fig. 12(b) allows for a tether or an antenna for shallow-water wireless control.

Fig. 12. (a) 3-D wire mesh view of *Huygens*. (b) A side view of *Huygens* prototype. Three transducers are installed on the shell with two at the frontal "eyes" positioned for steering and another in the rear for forward thrust. Tethered signal generates a multiplexed 7MHz sinusoidal input to the three USTs.

explained by distortion in finite-amplitude traveling waves, according to weak shock theory. On the other hand, the fact that thrust in this case increases with input power despite the saturation of velocity highlights an unusual observation – that thrust production mechanism involves the wake only indirectly, and in a manner that is distinct from other propulsors. This fact may offer some interesting avenues for UST design, where the wake and the thrust force could be manipulated independently. This is especially useful in a scenario where larger thrust is desired but the wake has to be weak at the same time, for

In summary, increasing the output voltage of the power amplifier will no doubt increase the thrust and kinetic energy production of the transducer, but at the same time, introduces an undesirable disproportionate relationship (Tan & Hover, 2010a). This will be further

We designed and constructed a small, streamlined shell with three embedded UST devices for propulsion and steering in the horizontal plane. The shell measures 215mm160mm80mm, profiled by a truncated NACA 0054 airfoil in the side view, and a truncated NACA 0025 airfoil in the plan view, as shown in Fig. 12(a). The shell is made from high-strength urethane foam for buoyancy, and coated with polyurethane. A UST is positioned at the rear end of the craft to provide forward thrust, and two USTs subtending 120° are symmetrically located on each side of the front end – at the "fish eyes" position. Together, these provide the right/left steering and backing thrust. Inside the shell, two rectangular cavities are machined, measuring 100mm100mm35mm, and 45mm60mm30mm. The shell can be opened into two halves via a stepped mid-section opening, lined with double O-rings for a watertight seal. The cylindrical UST seats are also lined with O-rings. The vent shown in the top left corner of Fig. 12(b) allows for a tether or

(a) (b)

Fig. 12. (a) 3-D wire mesh view of *Huygens*. (b) A side view of *Huygens* prototype. Three transducers are installed on the shell with two at the frontal "eyes" positioned for steering and another in the rear for forward thrust. Tethered signal generates a multiplexed 7MHz

NACA 0025

example, to minimize stirring up particulates near the seabed.

discussed in Section 3.

Tether/ antenna

UST seat

**2.4 Small underwater vehicle,** *Huygens*

an antenna for shallow-water wireless control.

NACA 0054 UST seats

sinusoidal input to the three USTs.

#### **2.5 Ultrasonic propulsion design considerations**

To our knowledge, there are only three experimental works on ultrasonic propulsors reported from (Allison, et al., 2008), (Yu & Kim, 2004), and (Wang, et al., 2011); we compare them with our UST in terms of thrust density, scaled thrust density and power density, in Table 2. As our UST system was operating at a resonance frequency and high voltage, it is difficult to make a fair and direct comparison of performance. We have employed a much higher power level, resulting in a very high thrust level and higher scaled thrust density.

Table 2. Performance of different UST devices.

This latter property is important in applications because it indicates a very compact force source operating with reasonable voltage levels, exploitable to benefit from many of its unique ultrasonic attributes we discussed earlier in the introduction.

Fig. 13. Thrust force produced by the UST versus driving electrical power. The *l* and *h* subscripts indicate evident low- and high-power regimes. The output voltage to the sinusoid is 59Vrms, and for the square wave is 54Vrms.

Ultrasonic Thruster 161

and 1.00210-3kg/ms respectively. The parameter <sup>2</sup> Re *Cd* , solved using Eq. (10), is 23.4106, and for *Huygens*, a unique point can be identified on the Re *Cd* Moody diagram; Re = 1.17104 and 0.17 *Cd* . It is thus estimated that *Huygens* will advance at a velocity of

Regarding mission duration and length, a small 11V, 0.75Ah lithium-ion battery would occupy about 10% of the *Huygens* vehicle volume. We assume an average power capacity reduction of 90% in a single discharge cycle, providing about 7.4Wh of energy. The UST consumes 69W of electrical power with an acoustic efficiency of 33.6% (Fig. 13), to produce 13.5mN of thrust with a constant vehicle advance velocity of about 0.05m/s. If we assume the instrumentation and other loads are small compared to the propulsive load, a simple straight-path mission will last around six minutes and travel a distance of about twenty meters. A somewhat larger battery could power the vehicle for perhaps thirty minutes, with a mission length of one hundred meters. While the UST is clearly not competitive with rotary or some biomimetic propulsors in terms of transit efficiency, nonetheless these estimates show that maneuvering a very small-scale vehicle utilizing USTs offers a

(a) (b)

Battery

(c)

We have also demonstrated a wireless version of *Huygens* (Fig. 14(c)) powered by a small on board battery (Fig. 14(b)). However, the electronics board could only supply limited power to each UST, and was able to slowly move the vehicle but inadequate to overcome the

Fig. 14. (a) A specialized UST constructed from a one centimeter diameter piezoelectric transducer for underwater operation. (b) An internal view of the components of the wireless

underwater vehicle, *Huygens*. (c) Wireless testing of *Huygens* in a laboratory tank.

0.054m/s – very close to the observed value.

propulsive force with interesting thrust and wake characteristics.

Fig. 13 details the acoustic efficiency of the UST transmitting at a sinusoidal 7MHz. From Eq. (2), *T* = *P*/*c*, where *c* is known (1480m/s), and *T* and *P* are measured. It can be made out that the sinusoidal waveform has two regimes relating thrust to electrical power – one of lower power with proportionally increasing thrust, and another somewhat saturated thrust at higher power. Below 70W electrical power, the power-thrust curve for sinusoidal input shows an acoustic efficiency of about 34%. Above 70W, the UST efficiency falls to less than 10%. Efficiency is calculated incrementally for each of the lines, that is, using the change in thrust versus the change in power. A square waveform is added in Fig. 13 for the sake of comparison. In general, the sinusoidal excitation is much more efficient than the square waveform. We note that the efficiency numbers given in (Allison, et al., 2008) are somewhat higher than what we show here, in part because of their custom transducer design, but also because they operated at much lower power levels. Below 2mN, we also achieve high efficiency around 70%. In respect to improving acoustic efficiency, other features such as nozzle appendages, shaping of UST, stacked piezoelectric layers could be considered.

#### **2.5.1 Vehicle mission**

In this subsection, we infer the expected speed and mission length that could reasonably be achieved from a UST-propelled underwater vehicle similar to *Huygens*. For our vehicle speed measurements, we used a high resolution Vision Research digital camera (Phantom V10) mounted with a wide-angle 20mm lens from Sigma. We sampled the advance speed of *Huygens* at 40samples/second over a straight course of 0.6m; the craft was allowed to accelerate for ten seconds before beginning the velocity measurement. Although a tether was attached to the vehicle for these tests, we maintained a large loop hanging below the vehicle, and moved the top of the tether along with the vehicle, using a sliding car and guiding post. With the recorded images of *Huygens*, the advance speed measured is a constant 0.049m/s.

The vehicle is quite streamlined, with only small holes around the frontal USTs, and a flat trim at the rear. From the top sectional view of *Huygens*, we can approximate the overall profile as an airfoil with a thickness-to-chord ratio of 0.37, and a span of 0.16m. The Reynolds number is Re *U lc* , where (kg/m3), *U* (m/s), *lc* (m) and (kg/ms) denote the fluid density, advance speed of the vehicle, chord length of the vehicle, and dynamic viscosity of the fluid respectively. The drag coefficient is 2 2 *d w <sup>T</sup> <sup>C</sup> A U* , where *T* (N) and *Aw*

(m3) denote the thrust force, and wetted surface area respectively. Expressing *U* on the left hand side of Re and *Cd* separately, the Reynolds number and drag coefficient is related by

$$\text{Re}^2 \, \text{C}\_d = \frac{2 \, \rho \, l\_c^2 \, T}{A\_w \, \mu^2} \,. \tag{10}$$

Using the Moody chart for a streamlined strut (Hoerner, 1965), *U* can then be estimated. To obtain the thrust, we recall that a sinusoidal input at 7MHz and 59Vrms, creates a thrust force of *T* = 13.5mN (Fig. 11(a)). The constants , *lc*, *Aw*, and are 1000kg/m3, 0.215m, 0.053m2,

Fig. 13 details the acoustic efficiency of the UST transmitting at a sinusoidal 7MHz. From Eq.