Aspectos técnicos fundamentales de los regímenes en vigencia

Although known for many decades, sound- and ultrasound-assisted drying has recently found renewed interest mostly because of the significant progress in nonthermal dewatering (Mujumdar, 1991; Muralidhara and Lockhart, 1988). Sound is a special form of energy transmitted via pressure fluctuations in air, water, or other elastic media. Any displacement of a particle of this elastic medium from its mean position results in an instantaneous increase in pressure. When leveling, this pressure peak restores the particle to its original position, but also passes on the disturbance to the next particle. The cycles of pressure increase (compression) and decrease (rarefaction) propagate through the me- dium as a sound wave.

On a microscale, sound is characterized by pressure and particle veloc- ity. The product of these two parameters is called sound intensity—a vector quantity that describes the rate of energy flow through a unit surface area normal to the direction of sound propagation

Sound intensity⫽ Pressure ⫻ Particle velocity

(13.1) ⫽Force Area ⫻ Distance Time ⫽ Energy Area⫻ Time⫽ Power Area 187

FIGURE13.1 Sound intensity around the point source of acoustic energy.

As seen from Figure 13.1, sound generated by a point source with power

W propagates as a spherical wave so the sound intensity is inversely propor-

tional to the square of a distance from the sound source.

The variations of both pressure and velocity follow a sinusoid; if they are in phase the peak pressure occurs at the same time as a peak in the particle velocity, and the product of these two gives the intensity, which is not only the maximum instantaneous intensity but also the maximum time-averaged intensity (Figure 13.2). At the other extreme, when pressure and velocity are out of phase, the time-averaged intensity is zero. Phase compatibility is ex- tremely important in drying since processes, which affect drying rate (e.g., cavitation), depend on the sound intensity.

On a macroscale, sound is primarily characterized by the frequency ( f ), which relates the speed of wave propagation (u) (sound velocity) to the wave- length (λ):

f⫽u

λ (13.2)

The second main quantity used to characterize sound on a macroscale is the amplitude of the pressure fluctuations expressed as the sound pressure level (SPL) on the decibel (dB) scale with 20 Pa as reference level. Because the sound pressure depends on the distance from the source generating given sound power (energy per unit time) and on the acoustic environment (sound

FIGURE13.2 Time-averaged sound intensity versus phase shift.

field), it is then frequently quantified in terms of the sound intensity. Because of the large range of sound intensity, it is also given on a decibel scale but

with 1 pW/m2 _{as the reference level. The relations between sound power,}

sound intensity, and sound pressure are presented in Figure 13.3. The decibel scale is given in Table 13.1.

In a free acoustic field such as that in an open air or anechoic chamber, the pressure and intensity levels in the direction of propagation are numerically the same. In a diffuse field in which sound is reflected so many times that it travels in all directions with equal magnitude and probability (reverberation chamber), the pressure and intensity levels are different and this difference is known as the pressure-intensity index (phase index or reactivity index).

Aside from the frequency and sound intensity, the key point in the design of sound-assisted dryers is the mode of energy propagation. Sound energy can be propagated as longitudinal waves (also called compression waves) or transverse waves for which vibration of the particle in the material occurs

FIGURE13.3 Decibel scale and the relation between the Sound Power Level (LW),

Sound Intensity Level (LI), and Sound Pressure Level (LP).

TABLE13.1 Decibel Scale

Units Pressure, N/m2 _{Decibels Sound source}

1 0.00002 0 Threshold of hearing 10 0.0002 20 Forest 100 0.002 40 Library 1,000 0.02 60 Normal conversation 10,000 0.2 80 Workshop 100,000 2 100 Pneumatic chipper 1,000,000 20 120 Jet takeoff 10,000,000 200 140 Threshold of pain

signed to accommodate longitudinal waves.

In a free space, the sound source can be considered as a point source (see Figure 13.1). In practical industrial applications, however, sound is either radiated from the source of definite size (e.g., loudspeaker membrane) or, more frequently, reflected from the point source by surfaces of different shapes such as horn, paraboloid, ellipsoid, etc. In both cases such sound radiation can be regarded as coming from a plane source. This results in a specific pattern of sound intensity; in the zone near the sound source, the sound intensity is con- stant (Fresnel zone), whereas outside this zone (the Fraunhofer zone) the sound intensity decreases inversely with the square of the distance from the plane source, i.e., in the same way as for a point source (Figure 13.4).

In some configurations of dryers the length of zones and thus the sound intensity distribution may become important. For example, the Fresnel zone for the plane source 10 cm in diameter is negligible (couple of millimeters) for sound at 100 Hz (cf. frequency of pulse combustion) but extends for 15.6 cm in the range of ultrasound at 20 kHz and 31.2 cm at 40 kHz.

According to the frequency of pressure pulsation, sound can be classified

as infrasound ( f⬍ 20 Hz), sound (audible) (20 Hz ⬍ f ⬍ 20 kHz), and ultra-

sound ( f⬍ 20 kHz). In the past, the R&D were targeted at frequencies over 15 kHz. The newly developed pulse combustion technique has, however, shifted the frequency range toward lower frequency (Kudra and Mujumdar, 1995), in the order of 50 to 200 Hz (see Chapter 14). Also, interesting labora- tory results were reported in the range of infrasound (Kudra, 1998; Woods, 1991; Woods, 1992) (see Chapter 26).

Ultrasonic applications are rigidly classified into low and high intensity. Low-intensity applications are made typically in the mega-Hertz frequencies and acoustic power up to tens of milliwatts, and usually do not alter material properties under operation. In contrast, the high-intensity ultrasound is gener- ally used for changing the properties of the material through which it is passed or altering the physical–chemical processes. High-intensity applications are made at low frequencies, about 20 to 40 kHz, and these are used in drying and dewatering.

13.2

SOUND GENERATION

In industrial applications sound waves are generated by a transducer, which converts the original form of energy to the energy of oscillatory motion. Such transducers are classified into six main groups:

1. Piezoelectric, in which periodic changes in physical size of certain crystals (such as quartz, tourmaline, and zinc oxide) due to applied electric potential generates mechanical vibrations, which are propagated as sound waves. Used in the range from 20 kHz to 10 GHz.

2. Magnetostrictive, in which mechanical vibrations are caused by

changes in the physical size of certain metals such as nickel, cobalt, or iron, or certain nonmetals known as ferrites due to external magnetic field. Used in the range of 40 to 100 kHz.

3. Electromagnetic, in which the vibration of a solid armature (e.g.,

membrane in loudspeakers and microphones) is due to coupled electric and

magnetic fields. Used at f⬍ 50 kHz.

4. Electrostatic, in which the periodic variation of charges in an electri-

cal capacitor of a special design induces mechanical vibration. Used at f⬍

100 kHz.

5. Mechanical, in which sound waves are generated due to the action

of a truly mechanical device such as rotating counterbalanced weights or a mechanical device energized by the kinetic energy of the working fluid (sirens

and whistles). Used at f⬍ 50 kHz.

6. Miscellaneous, in which thermal, chemical, optical, and other phe-