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Drying with Shock WavesOne of the i
Drying with Shock Waves
One of the innovative technologies for atomizing viscous liquids and thin pasty
materials in a gas is the use of shock waves. This method could be used in
spray drying to disperse the liquid feed (see Chapter 14) and thus eliminate
the conventional atomizer from the system. This will avoid problems with
erosion in disk atomizers and clogging of single- or two-stream spray nozzles.
Potential applications of this idea in other types of dryers for dispersed materials
include pneumatic, ring, spin-flash, and vortex dryers, in which the momentum
of shock waves can enhance the hydrodynamic impact of a conventional
gas-carrier.
It should be noted that the term ‘‘shock waves’’ refers to a pressure
wave of large amplitude that arises from sharp and violent disturbances when
the velocity of wave propagation exceeds the velocity of sound propagation.
Characteristically, an abrupt change of the medium properties (e.g., pressure,
stress, density, particle velocity, temperature, etc.) takes place in a limited
space across the shock wave (Schetz and Fuhs, 1996; Shapiro, 1953; Anderson,
1982; Saad, 1992). In the case described in this chapter, the physical
phenomenon of shock wave is restricted to one-dimensional plane wave propagation,
in which properties of air in the resonant tube of the wave generator
131
132 Chapter 10
vary with respect to only one spatial coordinate and time. Although it is technically
feasible to generate a true shock wave by moving a piston into a compressible
medium, the velocity of wave propagation in the system presented
here is lower than the sonic velocity. However, the almost flat pressure profile
at the front of the wave exiting the generator is similar to a nearly discontinuous
shock front propagating at a supersonic velocity. Because there is no adequate
definition for the pressure wave of such characteristics, the term ‘‘shock
wave’’ will be used throughout this chapter.
Atomization and drying in shock waves is still at the development stage,
e.g., laboratory- and pilot-scale experiments. Figure 10.1 presents schematically
the experimental shock-wave generator used by Lyulin (1998) to disperse
pasty materials in a spray dyer. The generator consists of a stainless steel tube
0.04 m in diameter, which propagates the pressure waves and serves as a
quarter-wave (Helmholtz) resonator (see Chapter 14). One end of the resonance
tube is open to the atmosphere while the other is connected to a pulse
generator through a truncated cone 0.2 m long. The generator comprises a
cylindrical chamber 0.08 m in internal diameter and a crankshaft-connecting
rod assembly, which moves the piston in a reciprocating manner. The stroke
of the piston is 0.082 m. The pulse generator is driven by a 7-kW DC motor
with controllable rotational speed allowing variable frequency of the strokes
from 7 to 28 Hz.
FIGURE 10.1 Schematic of the experimental shock-wave generator. (From Lyulin,
1998.)
Drying with Shock Waves 133
The instantaneous pressure and velocity distributions along the resonance
tube are monitored by piezoelectric transducers and hot-wire thermal
anemometer that are connected to the oscilloscope and photo film recorder.
These make possible the tuning of the generator to the acoustic resonance by
varying the rotational speed of the crankshaft. Also, there is a provision to
attach resonance tubes of various lengths and diameters to obtain required
amplitudes of pressure and velocity pulsations.
Figure 10.2 presents a typical temporal pressure oscillation at various
points along the resonance tube. It is clear that the profile of pressure oscillation
near the piston is sinusoidal because of the reciprocating movement of
the piston. As the pressure wave travels along the resonant tube, its descending
part (the front of the wave) becomes shorter while the ascending one (the
tail of the wave) levels off gradually, giving finally a steep pressure front
characteristic of a shock wave. The extremely high gradients of pressure at
the front of the plane wave not only initiate mechanical effects such as liquid
dispersion but also can alter drying rates due to enhanced evaporation and
capillary flow of liquid and vapor moisture.
Unlike pressure, the profile of the velocity pulsation remains practically
unchanged along the resonant tube and distortion of the sinusoidal velocity
pulsation occurs only at the tube outlet. As shown in Figure 10.3, the amplitude
of velocity pulsation decreases sharply with the distance of wave propagation
in open air. To take full advantage of the momentum of shock waves, liquid
to be dispersed should be fed close to the outlet from the resonant tube, in
this case up to about 20 cm. Also, the strongest impact of shock wave due to
air velocity might be expected over a distance up to 1 m from the resonance
tube.
Figure 10.4 presents amplitude-frequency characteristics of two different
resonant tubes, where the first and second resonance frequencies are clearly
identified by the consecutive maxima on the respective curves.
For a given tube length, the resonance frequency is calculated as
fr (2n 1)
v
4Lt
(10.1)
where v is the velocity of sound propagation, Lt is the tube length, and n is
the order of the harmonic frequency.
From Eq. (10.1) it follows that the product fr Lt does not depend on the
tube diameter but is a constant characteristic of the gaseous environment.
Hence, at the sound velocity in air equal to 330 m/s, the first resonance is
obtained at fr Lt 82.5 m/s.
134 Chapter 10
FIGURE 10.2 Characteristic of pressure oscillation in the resonance tube.
Drying with Shock Waves 135
FIGURE 10.3 Variation of the amplitude of the pulsating velocity with distance from
the outlet of the resonance tube.
The maximum amplitude of the velocity pulsation appears at n 1
(Figure 10.4). It is quite reasonable to assume that the amplitude of air pulsation
at the tube outlet is proportional to the amplitude of the velocity of piston
movement
u Kuc (10.2)
Accounting for the different diameters of the resonant tube (dt ) and substituting
uc by (πfs), the following equation (valid for u 140 m/s) was
derived by Lyulin (1998):
u Zπfs
dc
dt
(10.3)
where s is the piston stroke length, dc is the piston diameter, and Z is a constant
equal to 11.0 for 0.044 dt 0.005 m and equal to 9.1 for 0.033 dt
0.044 m. These values were determined experimentally.
136 Chapter 10
FIGURE 10.4 Typical resonance characteristics of the shock-wave generator. (From
Lyulin, 1998.)
Expressing the frequency in terms of the crankshaft rpm, the following
experimental correlation can be used to calculate the length of the resonant
tube and the amplitude of air velocity at the tube outlet:
u 0.0523ZsN dc
dt, m/s and Lt
15v
N
, m (10.4)
The shock wave acts as a liquid atomizer up to the point at which the
momentum of the shock wave is able to disperse the liquid stream. By analogy
with two-phase flow in packed columns, such hydrodynamic conditions can
be construed as ‘‘flooding.’’ Hence, the region of stable atomization is mapped
in terms of a flooding coefficient, defined as the mass flow ratio of undispersed
liquid to the total liquid subject to the shock-wave field
β
W Wd
W
(10.5)
Drying with Shock Waves 137
Lyulin (1998) provided the following empirical correlation for the flooding
coefficient:
β 1 A
ug
ul dt
dl2
(10.6)
where A is the constant, dl is the diameter of the liquid jet subject to atomization,
and ul and ug are the liquid jet velocity and the amplitude of the gas
velocity pulsation, respectively.
Thus, the generalized correlation for the flooding velocity shown in Figure
10.5 is
ul 0.00161 f 1.31 (ug 37.3)1/3
d0.25
l
(10.7)
where the liquid jet diameter dl is in mm, frequency f is in Hz, and the gas
velocity ug is in m/s.
The dispersion of pasty pigments with shock waves was studied experimentally
using the shock-wave generator with a resonance tube of 0.033 m.
This allows achieving air velocity equal to 163 m/s at 19.8 Hz of the reciprocating
movement of the piston. The pasty feed was located 0.05 m from the
resonance tube outlet at its axis. Such a distance was found to be optimal over
the range from 1.5 to 5 times the tube diameter.
The following procedure was used to obtain a droplet size distribution
(Muranov et al., 1997). Dispersed pigments were trapped in a filter paper
placed perpendicularly to the tube axis 1 m from the pasty feed. Segments of
the filter paper with spots of droplets were then analyzed under a microscope,
and about 2000 droplets were counted for the size distribution. Knowing the
dry mass of the dispersed pigment (m) and total surface area of the spots (SS ),
the volume of the droplet having (X, % wb) moisture content that leaves the
spot with diameter (dS ) can be calculated from
Vp
πd2S
4ρm
m
SS
100
100 X
(10.8)
where ρm is a density of the wet material.
Thus, the droplet diameter is
dp 6Vp
π 1/3
150d2S
m
SS(100 X)ρm1/3
(10.9)
FIGURE 10.5 Flooding curve for atomizing liquids with shock waves. (From Lyulin,
1998.)
Drying with Shock Waves 139
whereas the total surface area of dispersed liquid trapped in the filter paper
is
S n
i1
Sd,i n
i1
π(d2p
)i (10.10)
Typical distribution of droplet size for anticorrosive paint based on zinc
phosphate is shown in Figure 10.6. The symbol dM identifies here the median
diameter (midpoint of the size distribution) and dsV is the surface volume diameter,
i.e., diameter of the sphere having the same ratio of surface area-tovolume
as the droplet, and calculated as
dsV
Σd3i
ni
Σd2i
ni
(10.11)
Figure 10.6 indicates that droplets generated by the shock wave are
nearly monodispersed since the mass fraction of droplets larger than 27 μm is
negligible compared to the m
One of the innovative technologies for atomizing viscous liquids and thin pasty
materials in a gas is the use of shock waves. This method could be used in
spray drying to disperse the liquid feed (see Chapter 14) and thus eliminate
the conventional atomizer from the system. This will avoid problems with
erosion in disk atomizers and clogging of single- or two-stream spray nozzles.
Potential applications of this idea in other types of dryers for dispersed materials
include pneumatic, ring, spin-flash, and vortex dryers, in which the momentum
of shock waves can enhance the hydrodynamic impact of a conventional
gas-carrier.
It should be noted that the term ‘‘shock waves’’ refers to a pressure
wave of large amplitude that arises from sharp and violent disturbances when
the velocity of wave propagation exceeds the velocity of sound propagation.
Characteristically, an abrupt change of the medium properties (e.g., pressure,
stress, density, particle velocity, temperature, etc.) takes place in a limited
space across the shock wave (Schetz and Fuhs, 1996; Shapiro, 1953; Anderson,
1982; Saad, 1992). In the case described in this chapter, the physical
phenomenon of shock wave is restricted to one-dimensional plane wave propagation,
in which properties of air in the resonant tube of the wave generator
131
132 Chapter 10
vary with respect to only one spatial coordinate and time. Although it is technically
feasible to generate a true shock wave by moving a piston into a compressible
medium, the velocity of wave propagation in the system presented
here is lower than the sonic velocity. However, the almost flat pressure profile
at the front of the wave exiting the generator is similar to a nearly discontinuous
shock front propagating at a supersonic velocity. Because there is no adequate
definition for the pressure wave of such characteristics, the term ‘‘shock
wave’’ will be used throughout this chapter.
Atomization and drying in shock waves is still at the development stage,
e.g., laboratory- and pilot-scale experiments. Figure 10.1 presents schematically
the experimental shock-wave generator used by Lyulin (1998) to disperse
pasty materials in a spray dyer. The generator consists of a stainless steel tube
0.04 m in diameter, which propagates the pressure waves and serves as a
quarter-wave (Helmholtz) resonator (see Chapter 14). One end of the resonance
tube is open to the atmosphere while the other is connected to a pulse
generator through a truncated cone 0.2 m long. The generator comprises a
cylindrical chamber 0.08 m in internal diameter and a crankshaft-connecting
rod assembly, which moves the piston in a reciprocating manner. The stroke
of the piston is 0.082 m. The pulse generator is driven by a 7-kW DC motor
with controllable rotational speed allowing variable frequency of the strokes
from 7 to 28 Hz.
FIGURE 10.1 Schematic of the experimental shock-wave generator. (From Lyulin,
1998.)
Drying with Shock Waves 133
The instantaneous pressure and velocity distributions along the resonance
tube are monitored by piezoelectric transducers and hot-wire thermal
anemometer that are connected to the oscilloscope and photo film recorder.
These make possible the tuning of the generator to the acoustic resonance by
varying the rotational speed of the crankshaft. Also, there is a provision to
attach resonance tubes of various lengths and diameters to obtain required
amplitudes of pressure and velocity pulsations.
Figure 10.2 presents a typical temporal pressure oscillation at various
points along the resonance tube. It is clear that the profile of pressure oscillation
near the piston is sinusoidal because of the reciprocating movement of
the piston. As the pressure wave travels along the resonant tube, its descending
part (the front of the wave) becomes shorter while the ascending one (the
tail of the wave) levels off gradually, giving finally a steep pressure front
characteristic of a shock wave. The extremely high gradients of pressure at
the front of the plane wave not only initiate mechanical effects such as liquid
dispersion but also can alter drying rates due to enhanced evaporation and
capillary flow of liquid and vapor moisture.
Unlike pressure, the profile of the velocity pulsation remains practically
unchanged along the resonant tube and distortion of the sinusoidal velocity
pulsation occurs only at the tube outlet. As shown in Figure 10.3, the amplitude
of velocity pulsation decreases sharply with the distance of wave propagation
in open air. To take full advantage of the momentum of shock waves, liquid
to be dispersed should be fed close to the outlet from the resonant tube, in
this case up to about 20 cm. Also, the strongest impact of shock wave due to
air velocity might be expected over a distance up to 1 m from the resonance
tube.
Figure 10.4 presents amplitude-frequency characteristics of two different
resonant tubes, where the first and second resonance frequencies are clearly
identified by the consecutive maxima on the respective curves.
For a given tube length, the resonance frequency is calculated as
fr (2n 1)
v
4Lt
(10.1)
where v is the velocity of sound propagation, Lt is the tube length, and n is
the order of the harmonic frequency.
From Eq. (10.1) it follows that the product fr Lt does not depend on the
tube diameter but is a constant characteristic of the gaseous environment.
Hence, at the sound velocity in air equal to 330 m/s, the first resonance is
obtained at fr Lt 82.5 m/s.
134 Chapter 10
FIGURE 10.2 Characteristic of pressure oscillation in the resonance tube.
Drying with Shock Waves 135
FIGURE 10.3 Variation of the amplitude of the pulsating velocity with distance from
the outlet of the resonance tube.
The maximum amplitude of the velocity pulsation appears at n 1
(Figure 10.4). It is quite reasonable to assume that the amplitude of air pulsation
at the tube outlet is proportional to the amplitude of the velocity of piston
movement
u Kuc (10.2)
Accounting for the different diameters of the resonant tube (dt ) and substituting
uc by (πfs), the following equation (valid for u 140 m/s) was
derived by Lyulin (1998):
u Zπfs
dc
dt
(10.3)
where s is the piston stroke length, dc is the piston diameter, and Z is a constant
equal to 11.0 for 0.044 dt 0.005 m and equal to 9.1 for 0.033 dt
0.044 m. These values were determined experimentally.
136 Chapter 10
FIGURE 10.4 Typical resonance characteristics of the shock-wave generator. (From
Lyulin, 1998.)
Expressing the frequency in terms of the crankshaft rpm, the following
experimental correlation can be used to calculate the length of the resonant
tube and the amplitude of air velocity at the tube outlet:
u 0.0523ZsN dc
dt, m/s and Lt
15v
N
, m (10.4)
The shock wave acts as a liquid atomizer up to the point at which the
momentum of the shock wave is able to disperse the liquid stream. By analogy
with two-phase flow in packed columns, such hydrodynamic conditions can
be construed as ‘‘flooding.’’ Hence, the region of stable atomization is mapped
in terms of a flooding coefficient, defined as the mass flow ratio of undispersed
liquid to the total liquid subject to the shock-wave field
β
W Wd
W
(10.5)
Drying with Shock Waves 137
Lyulin (1998) provided the following empirical correlation for the flooding
coefficient:
β 1 A
ug
ul dt
dl2
(10.6)
where A is the constant, dl is the diameter of the liquid jet subject to atomization,
and ul and ug are the liquid jet velocity and the amplitude of the gas
velocity pulsation, respectively.
Thus, the generalized correlation for the flooding velocity shown in Figure
10.5 is
ul 0.00161 f 1.31 (ug 37.3)1/3
d0.25
l
(10.7)
where the liquid jet diameter dl is in mm, frequency f is in Hz, and the gas
velocity ug is in m/s.
The dispersion of pasty pigments with shock waves was studied experimentally
using the shock-wave generator with a resonance tube of 0.033 m.
This allows achieving air velocity equal to 163 m/s at 19.8 Hz of the reciprocating
movement of the piston. The pasty feed was located 0.05 m from the
resonance tube outlet at its axis. Such a distance was found to be optimal over
the range from 1.5 to 5 times the tube diameter.
The following procedure was used to obtain a droplet size distribution
(Muranov et al., 1997). Dispersed pigments were trapped in a filter paper
placed perpendicularly to the tube axis 1 m from the pasty feed. Segments of
the filter paper with spots of droplets were then analyzed under a microscope,
and about 2000 droplets were counted for the size distribution. Knowing the
dry mass of the dispersed pigment (m) and total surface area of the spots (SS ),
the volume of the droplet having (X, % wb) moisture content that leaves the
spot with diameter (dS ) can be calculated from
Vp
πd2S
4ρm
m
SS
100
100 X
(10.8)
where ρm is a density of the wet material.
Thus, the droplet diameter is
dp 6Vp
π 1/3
150d2S
m
SS(100 X)ρm1/3
(10.9)
FIGURE 10.5 Flooding curve for atomizing liquids with shock waves. (From Lyulin,
1998.)
Drying with Shock Waves 139
whereas the total surface area of dispersed liquid trapped in the filter paper
is
S n
i1
Sd,i n
i1
π(d2p
)i (10.10)
Typical distribution of droplet size for anticorrosive paint based on zinc
phosphate is shown in Figure 10.6. The symbol dM identifies here the median
diameter (midpoint of the size distribution) and dsV is the surface volume diameter,
i.e., diameter of the sphere having the same ratio of surface area-tovolume
as the droplet, and calculated as
dsV
Σd3i
ni
Σd2i
ni
(10.11)
Figure 10.6 indicates that droplets generated by the shock wave are
nearly monodispersed since the mass fraction of droplets larger than 27 μm is
negligible compared to the m
0/5000
Drying with Shock WavesOne of the innovative technologies for atomizing viscous liquids and thin pastymaterials in a gas is the use of shock waves. This method could be used inspray drying to disperse the liquid feed (see Chapter 14) and thus eliminatethe conventional atomizer from the system. This will avoid problems witherosion in disk atomizers and clogging of single- or two-stream spray nozzles.Potential applications of this idea in other types of dryers for dispersed materialsinclude pneumatic, ring, spin-flash, and vortex dryers, in which the momentumof shock waves can enhance the hydrodynamic impact of a conventionalgas-carrier.It should be noted that the term ‘‘shock waves’’ refers to a pressurewave of large amplitude that arises from sharp and violent disturbances whenthe velocity of wave propagation exceeds the velocity of sound propagation.Characteristically, an abrupt change of the medium properties (e.g., pressure,stress, density, particle velocity, temperature, etc.) takes place in a limitedspace across the shock wave (Schetz and Fuhs, 1996; Shapiro, 1953; Anderson,1982; Saad, 1992). In the case described in this chapter, the physicalphenomenon of shock wave is restricted to one-dimensional plane wave propagation,in which properties of air in the resonant tube of the wave generator131132 Chapter 10vary with respect to only one spatial coordinate and time. Although it is technicallyfeasible to generate a true shock wave by moving a piston into a compressiblemedium, the velocity of wave propagation in the system presentedhere is lower than the sonic velocity. However, the almost flat pressure profileat the front of the wave exiting the generator is similar to a nearly discontinuousshock front propagating at a supersonic velocity. Because there is no adequatedefinition for the pressure wave of such characteristics, the term ‘‘shockwave’’ will be used throughout this chapter.Atomization and drying in shock waves is still at the development stage,e.g., laboratory- and pilot-scale experiments. Figure 10.1 presents schematicallythe experimental shock-wave generator used by Lyulin (1998) to dispersepasty materials in a spray dyer. The generator consists of a stainless steel tube0.04 m in diameter, which propagates the pressure waves and serves as aquarter-wave (Helmholtz) resonator (see Chapter 14). One end of the resonancetube is open to the atmosphere while the other is connected to a pulsegenerator through a truncated cone 0.2 m long. The generator comprises acylindrical chamber 0.08 m in internal diameter and a crankshaft-connectingrod assembly, which moves the piston in a reciprocating manner. The strokeof the piston is 0.082 m. The pulse generator is driven by a 7-kW DC motorwith controllable rotational speed allowing variable frequency of the strokesfrom 7 to 28 Hz.
FIGURE 10.1 Schematic of the experimental shock-wave generator. (From Lyulin,
1998.)
Drying with Shock Waves 133
The instantaneous pressure and velocity distributions along the resonance
tube are monitored by piezoelectric transducers and hot-wire thermal
anemometer that are connected to the oscilloscope and photo film recorder.
These make possible the tuning of the generator to the acoustic resonance by
varying the rotational speed of the crankshaft. Also, there is a provision to
attach resonance tubes of various lengths and diameters to obtain required
amplitudes of pressure and velocity pulsations.
Figure 10.2 presents a typical temporal pressure oscillation at various
points along the resonance tube. It is clear that the profile of pressure oscillation
near the piston is sinusoidal because of the reciprocating movement of
the piston. As the pressure wave travels along the resonant tube, its descending
part (the front of the wave) becomes shorter while the ascending one (the
tail of the wave) levels off gradually, giving finally a steep pressure front
characteristic of a shock wave. The extremely high gradients of pressure at
the front of the plane wave not only initiate mechanical effects such as liquid
dispersion but also can alter drying rates due to enhanced evaporation and
capillary flow of liquid and vapor moisture.
Unlike pressure, the profile of the velocity pulsation remains practically
unchanged along the resonant tube and distortion of the sinusoidal velocity
pulsation occurs only at the tube outlet. As shown in Figure 10.3, the amplitude
of velocity pulsation decreases sharply with the distance of wave propagation
in open air. To take full advantage of the momentum of shock waves, liquid
to be dispersed should be fed close to the outlet from the resonant tube, in
this case up to about 20 cm. Also, the strongest impact of shock wave due to
air velocity might be expected over a distance up to 1 m from the resonance
tube.
Figure 10.4 presents amplitude-frequency characteristics of two different
resonant tubes, where the first and second resonance frequencies are clearly
identified by the consecutive maxima on the respective curves.
For a given tube length, the resonance frequency is calculated as
fr (2n 1)
v
4Lt
(10.1)
where v is the velocity of sound propagation, Lt is the tube length, and n is
the order of the harmonic frequency.
From Eq. (10.1) it follows that the product fr Lt does not depend on the
tube diameter but is a constant characteristic of the gaseous environment.
Hence, at the sound velocity in air equal to 330 m/s, the first resonance is
obtained at fr Lt 82.5 m/s.
134 Chapter 10
FIGURE 10.2 Characteristic of pressure oscillation in the resonance tube.
Drying with Shock Waves 135
FIGURE 10.3 Variation of the amplitude of the pulsating velocity with distance from
the outlet of the resonance tube.
The maximum amplitude of the velocity pulsation appears at n 1
(Figure 10.4). It is quite reasonable to assume that the amplitude of air pulsation
at the tube outlet is proportional to the amplitude of the velocity of piston
movement
u Kuc (10.2)
Accounting for the different diameters of the resonant tube (dt ) and substituting
uc by (πfs), the following equation (valid for u 140 m/s) was
derived by Lyulin (1998):
u Zπfs
dc
dt
(10.3)
where s is the piston stroke length, dc is the piston diameter, and Z is a constant
equal to 11.0 for 0.044 dt 0.005 m and equal to 9.1 for 0.033 dt
0.044 m. These values were determined experimentally.
136 Chapter 10
FIGURE 10.4 Typical resonance characteristics of the shock-wave generator. (From
Lyulin, 1998.)
Expressing the frequency in terms of the crankshaft rpm, the following
experimental correlation can be used to calculate the length of the resonant
tube and the amplitude of air velocity at the tube outlet:
u 0.0523ZsN dc
dt, m/s and Lt
15v
N
, m (10.4)
The shock wave acts as a liquid atomizer up to the point at which the
momentum of the shock wave is able to disperse the liquid stream. By analogy
with two-phase flow in packed columns, such hydrodynamic conditions can
be construed as ‘‘flooding.’’ Hence, the region of stable atomization is mapped
in terms of a flooding coefficient, defined as the mass flow ratio of undispersed
liquid to the total liquid subject to the shock-wave field
β
W Wd
W
(10.5)
Drying with Shock Waves 137
Lyulin (1998) provided the following empirical correlation for the flooding
coefficient:
β 1 A
ug
ul dt
dl2
(10.6)
where A is the constant, dl is the diameter of the liquid jet subject to atomization,
and ul and ug are the liquid jet velocity and the amplitude of the gas
velocity pulsation, respectively.
Thus, the generalized correlation for the flooding velocity shown in Figure
10.5 is
ul 0.00161 f 1.31 (ug 37.3)1/3
d0.25
l
(10.7)
where the liquid jet diameter dl is in mm, frequency f is in Hz, and the gas
velocity ug is in m/s.
The dispersion of pasty pigments with shock waves was studied experimentally
using the shock-wave generator with a resonance tube of 0.033 m.
This allows achieving air velocity equal to 163 m/s at 19.8 Hz of the reciprocating
movement of the piston. The pasty feed was located 0.05 m from the
resonance tube outlet at its axis. Such a distance was found to be optimal over
the range from 1.5 to 5 times the tube diameter.
The following procedure was used to obtain a droplet size distribution
(Muranov et al., 1997). Dispersed pigments were trapped in a filter paper
placed perpendicularly to the tube axis 1 m from the pasty feed. Segments of
the filter paper with spots of droplets were then analyzed under a microscope,
and about 2000 droplets were counted for the size distribution. Knowing the
dry mass of the dispersed pigment (m) and total surface area of the spots (SS ),
the volume of the droplet having (X, % wb) moisture content that leaves the
spot with diameter (dS ) can be calculated from
Vp
πd2S
4ρm
m
SS
100
100 X
(10.8)
where ρm is a density of the wet material.
Thus, the droplet diameter is
dp 6Vp
π 1/3
150d2S
m
SS(100 X)ρm1/3
(10.9)
FIGURE 10.5 Flooding curve for atomizing liquids with shock waves. (From Lyulin,
1998.)
Drying with Shock Waves 139
whereas the total surface area of dispersed liquid trapped in the filter paper
is
S n
i1
Sd,i n
i1
π(d2p
)i (10.10)
Typical distribution of droplet size for anticorrosive paint based on zinc
phosphate is shown in Figure 10.6. The symbol dM identifies here the median
diameter (midpoint of the size distribution) and dsV is the surface volume diameter,
i.e., diameter of the sphere having the same ratio of surface area-tovolume
as the droplet, and calculated as
dsV
Σd3i
ni
Σd2i
ni
(10.11)
Figure 10.6 indicates that droplets generated by the shock wave are
nearly monodispersed since the mass fraction of droplets larger than 27 μm is
negligible compared to the m
FIGURE 10.1 Schematic of the experimental shock-wave generator. (From Lyulin,
1998.)
Drying with Shock Waves 133
The instantaneous pressure and velocity distributions along the resonance
tube are monitored by piezoelectric transducers and hot-wire thermal
anemometer that are connected to the oscilloscope and photo film recorder.
These make possible the tuning of the generator to the acoustic resonance by
varying the rotational speed of the crankshaft. Also, there is a provision to
attach resonance tubes of various lengths and diameters to obtain required
amplitudes of pressure and velocity pulsations.
Figure 10.2 presents a typical temporal pressure oscillation at various
points along the resonance tube. It is clear that the profile of pressure oscillation
near the piston is sinusoidal because of the reciprocating movement of
the piston. As the pressure wave travels along the resonant tube, its descending
part (the front of the wave) becomes shorter while the ascending one (the
tail of the wave) levels off gradually, giving finally a steep pressure front
characteristic of a shock wave. The extremely high gradients of pressure at
the front of the plane wave not only initiate mechanical effects such as liquid
dispersion but also can alter drying rates due to enhanced evaporation and
capillary flow of liquid and vapor moisture.
Unlike pressure, the profile of the velocity pulsation remains practically
unchanged along the resonant tube and distortion of the sinusoidal velocity
pulsation occurs only at the tube outlet. As shown in Figure 10.3, the amplitude
of velocity pulsation decreases sharply with the distance of wave propagation
in open air. To take full advantage of the momentum of shock waves, liquid
to be dispersed should be fed close to the outlet from the resonant tube, in
this case up to about 20 cm. Also, the strongest impact of shock wave due to
air velocity might be expected over a distance up to 1 m from the resonance
tube.
Figure 10.4 presents amplitude-frequency characteristics of two different
resonant tubes, where the first and second resonance frequencies are clearly
identified by the consecutive maxima on the respective curves.
For a given tube length, the resonance frequency is calculated as
fr (2n 1)
v
4Lt
(10.1)
where v is the velocity of sound propagation, Lt is the tube length, and n is
the order of the harmonic frequency.
From Eq. (10.1) it follows that the product fr Lt does not depend on the
tube diameter but is a constant characteristic of the gaseous environment.
Hence, at the sound velocity in air equal to 330 m/s, the first resonance is
obtained at fr Lt 82.5 m/s.
134 Chapter 10
FIGURE 10.2 Characteristic of pressure oscillation in the resonance tube.
Drying with Shock Waves 135
FIGURE 10.3 Variation of the amplitude of the pulsating velocity with distance from
the outlet of the resonance tube.
The maximum amplitude of the velocity pulsation appears at n 1
(Figure 10.4). It is quite reasonable to assume that the amplitude of air pulsation
at the tube outlet is proportional to the amplitude of the velocity of piston
movement
u Kuc (10.2)
Accounting for the different diameters of the resonant tube (dt ) and substituting
uc by (πfs), the following equation (valid for u 140 m/s) was
derived by Lyulin (1998):
u Zπfs
dc
dt
(10.3)
where s is the piston stroke length, dc is the piston diameter, and Z is a constant
equal to 11.0 for 0.044 dt 0.005 m and equal to 9.1 for 0.033 dt
0.044 m. These values were determined experimentally.
136 Chapter 10
FIGURE 10.4 Typical resonance characteristics of the shock-wave generator. (From
Lyulin, 1998.)
Expressing the frequency in terms of the crankshaft rpm, the following
experimental correlation can be used to calculate the length of the resonant
tube and the amplitude of air velocity at the tube outlet:
u 0.0523ZsN dc
dt, m/s and Lt
15v
N
, m (10.4)
The shock wave acts as a liquid atomizer up to the point at which the
momentum of the shock wave is able to disperse the liquid stream. By analogy
with two-phase flow in packed columns, such hydrodynamic conditions can
be construed as ‘‘flooding.’’ Hence, the region of stable atomization is mapped
in terms of a flooding coefficient, defined as the mass flow ratio of undispersed
liquid to the total liquid subject to the shock-wave field
β
W Wd
W
(10.5)
Drying with Shock Waves 137
Lyulin (1998) provided the following empirical correlation for the flooding
coefficient:
β 1 A
ug
ul dt
dl2
(10.6)
where A is the constant, dl is the diameter of the liquid jet subject to atomization,
and ul and ug are the liquid jet velocity and the amplitude of the gas
velocity pulsation, respectively.
Thus, the generalized correlation for the flooding velocity shown in Figure
10.5 is
ul 0.00161 f 1.31 (ug 37.3)1/3
d0.25
l
(10.7)
where the liquid jet diameter dl is in mm, frequency f is in Hz, and the gas
velocity ug is in m/s.
The dispersion of pasty pigments with shock waves was studied experimentally
using the shock-wave generator with a resonance tube of 0.033 m.
This allows achieving air velocity equal to 163 m/s at 19.8 Hz of the reciprocating
movement of the piston. The pasty feed was located 0.05 m from the
resonance tube outlet at its axis. Such a distance was found to be optimal over
the range from 1.5 to 5 times the tube diameter.
The following procedure was used to obtain a droplet size distribution
(Muranov et al., 1997). Dispersed pigments were trapped in a filter paper
placed perpendicularly to the tube axis 1 m from the pasty feed. Segments of
the filter paper with spots of droplets were then analyzed under a microscope,
and about 2000 droplets were counted for the size distribution. Knowing the
dry mass of the dispersed pigment (m) and total surface area of the spots (SS ),
the volume of the droplet having (X, % wb) moisture content that leaves the
spot with diameter (dS ) can be calculated from
Vp
πd2S
4ρm
m
SS
100
100 X
(10.8)
where ρm is a density of the wet material.
Thus, the droplet diameter is
dp 6Vp
π 1/3
150d2S
m
SS(100 X)ρm1/3
(10.9)
FIGURE 10.5 Flooding curve for atomizing liquids with shock waves. (From Lyulin,
1998.)
Drying with Shock Waves 139
whereas the total surface area of dispersed liquid trapped in the filter paper
is
S n
i1
Sd,i n
i1
π(d2p
)i (10.10)
Typical distribution of droplet size for anticorrosive paint based on zinc
phosphate is shown in Figure 10.6. The symbol dM identifies here the median
diameter (midpoint of the size distribution) and dsV is the surface volume diameter,
i.e., diameter of the sphere having the same ratio of surface area-tovolume
as the droplet, and calculated as
dsV
Σd3i
ni
Σd2i
ni
(10.11)
Figure 10.6 indicates that droplets generated by the shock wave are
nearly monodispersed since the mass fraction of droplets larger than 27 μm is
negligible compared to the m
đang được dịch, vui lòng đợi..
Sấy với Waves Sốc Drying with Shock Waves
Một trong những công nghệ tiên tiến cho khâu nguyên tử hóa các chất lỏng nhớt và nhão mỏng One of the innovative technologies for atomizing viscous liquids and thin pasty
vật liệu trong một khí là việc sử dụng các sóng xung kích. Phương pháp này có thể được sử dụng trong materials in a gas is the use of shock waves. This method could be used in
sấy phun để giải tán các thức ăn lỏng (xem Chương 14) và do đó loại bỏ spray drying to disperse the liquid feed (see Chapter 14) and thus eliminate
phun thông thường từ hệ thống. Điều này sẽ tránh các vấn đề the conventional atomizer from the system. This will avoid problems with
xói mòn trong Atomizers đĩa và tắc nghẽn của các vòi phun đơn hoặc hai dòng. erosion in disk atomizers and clogging of single- or two-stream spray nozzles.
Ứng dụng tiềm năng của ý tưởng này trong các loại máy sấy vật liệu phân tán Potential applications of this idea in other types of dryers for dispersed materials
bao gồm khí nén, nhẫn, spin-flash và máy sấy xoáy, trong đó đà include pneumatic, ring, spin-flash, and vortex dryers, in which the momentum
của sóng xung kích có thể tăng cường tác động thủy động lực học của một quy ước of shock waves can enhance the hydrodynamic impact of a conventional
khí-carrier. gas-carrier.
Cần lưu ý rằng thuật ngữ '' sóng sốc '' là một áp lực It should be noted that the term ‘‘shock waves’’ refers to a pressure
sóng biên độ lớn nảy sinh từ các rối loạn sắc nét và bạo lực khi wave of large amplitude that arises from sharp and violent disturbances when
vận tốc truyền sóng vượt vận tốc của âm thanh lan truyền. the velocity of wave propagation exceeds the velocity of sound propagation.
Đặc trưng, một sự thay đổi đột ngột trong những tài sản trung bình (ví dụ, áp lực, Characteristically, an abrupt change of the medium properties (e.g., pressure,
căng thẳng, mật độ, vận tốc hạt, nhiệt độ, vv) diễn ra trong một giới hạn stress, density, particle velocity, temperature, etc.) takes place in a limited
không gian trên các sóng xung kích (Schetz và Fuhs, 1996; Shapiro, 1953; Anderson, space across the shock wave (Schetz and Fuhs, 1996; Shapiro, 1953; Anderson,
1982; Saad, 1992). Trong trường hợp được mô tả trong chương này, vật lý 1982; Saad, 1992). In the case described in this chapter, the physical
hiện tượng sóng xung kích được giới hạn cho một chiều truyền sóng máy bay, phenomenon of shock wave is restricted to one-dimensional plane wave propagation,
trong đó tính chất của không khí trong ống cộng hưởng của máy phát sóng in which properties of air in the resonant tube of the wave generator
131 131
132 Chương 10 132 Chapter 10
khác nhau đối với chỉ có một không gian phối hợp và thời gian. Mặc dù nó là kỹ thuật vary with respect to only one spatial coordinate and time. Although it is technically
khả thi để tạo ra một làn sóng sốc thật sự bằng cách di chuyển một piston vào một nén feasible to generate a true shock wave by moving a piston into a compressible
trung bình, vận tốc truyền sóng trong hệ thống được trình bày medium, the velocity of wave propagation in the system presented
ở đây là thấp hơn so với vận tốc âm thanh. Tuy nhiên, hồ sơ áp lực gần như bằng phẳng here is lower than the sonic velocity. However, the almost flat pressure profile
ở phía trước của sóng thoát khỏi máy phát điện là tương tự như một gần như liên tục at the front of the wave exiting the generator is similar to a nearly discontinuous
bị sốc trước tuyên truyền với vận tốc siêu âm. Vì không có đủ shock front propagating at a supersonic velocity. Because there is no adequate
định nghĩa cho các sóng áp suất của các đặc điểm như vậy, thuật ngữ '' sốc definition for the pressure wave of such characteristics, the term ‘‘shock
sóng '' sẽ được sử dụng trong suốt chương này. wave’’ will be used throughout this chapter.
Sương và sấy trong sóng xung kích vẫn đang ở giai đoạn phát triển, Atomization and drying in shock waves is still at the development stage,
ví dụ như, laboratory- và quy mô thí điểm thí nghiệm. Hình 10.1 trình bày sơ đồ e.g., laboratory- and pilot-scale experiments. Figure 10.1 presents schematically
máy phát điện giật sóng thử nghiệm được sử dụng bởi Lyulin (1998) để giải tán the experimental shock-wave generator used by Lyulin (1998) to disperse
các tài liệu nhão trong một Dyer phun. Các máy phát điện gồm một ống thép không gỉ pasty materials in a spray dyer. The generator consists of a stainless steel tube
0,04 m, đường kính, mà lan truyền sóng áp suất và phục vụ như là một 0.04 m in diameter, which propagates the pressure waves and serves as a
phần tư sóng (Helmholtz) cộng hưởng (xem Chương 14). Một đầu của sự cộng hưởng quarter-wave (Helmholtz) resonator (see Chapter 14). One end of the resonance
ống mở cửa để không khí trong khi khác được kết nối với một xung tube is open to the atmosphere while the other is connected to a pulse
máy phát điện thông qua một hình nón cụt dài 0,2 m. Các máy phát điện bao gồm một generator through a truncated cone 0.2 m long. The generator comprises a
buồng hình trụ 0,08 m, đường kính bên trong và một trục khuỷu-kết nối cylindrical chamber 0.08 m in internal diameter and a crankshaft-connecting
rod lắp ráp, trong đó di chuyển piston một cách qua lại. Các đột quỵ rod assembly, which moves the piston in a reciprocating manner. The stroke
của piston là 0,082 m. Máy phát xung được điều khiển bởi một 7-kW động cơ DC of the piston is 0.082 m. The pulse generator is driven by a 7-kW DC motor
với tốc độ quay cho phép kiểm soát tần số biến của các nét with controllable rotational speed allowing variable frequency of the strokes
7-28 Hz. from 7 to 28 Hz.
HÌNH 10.1 đồ của các máy phát điện giật sóng thử nghiệm. (Từ Lyulin, FIGURE 10.1 Schematic of the experimental shock-wave generator. (From Lyulin,
1998.) 1998.)
khô với Waves Sốc 133 Drying with Shock Waves 133
Áp lực và vận tốc tức thời phân bố dọc theo cộng hưởng The instantaneous pressure and velocity distributions along the resonance
ống được giám sát bởi các đầu dò áp điện và nhiệt nóng dây tube are monitored by piezoelectric transducers and hot-wire thermal
đo gió được kết nối với các dao động và hình ảnh ghi phim. anemometer that are connected to the oscilloscope and photo film recorder.
Những làm cho có thể điều chỉnh các máy phát điện để các cộng hưởng âm thanh bằng cách These make possible the tuning of the generator to the acoustic resonance by
thay đổi tốc độ quay của trục khuỷu. Ngoài ra, có một điều khoản để varying the rotational speed of the crankshaft. Also, there is a provision to
gắn ống cộng hưởng của chiều dài và đường kính khác nhau để có được yêu cầu attach resonance tubes of various lengths and diameters to obtain required
biên độ áp lực và vận tốc rung động. amplitudes of pressure and velocity pulsations.
Hình 10.2 trình bày một dao động áp lực thời gian điển hình tại nhiều Figure 10.2 presents a typical temporal pressure oscillation at various
điểm dọc theo ống cộng hưởng. Rõ ràng là hồ sơ cá nhân của dao động áp lực points along the resonance tube. It is clear that the profile of pressure oscillation
gần piston là hình sin vì sự chuyển động qua lại của near the piston is sinusoidal because of the reciprocating movement of
piston. Khi làn sóng áp lực di chuyển dọc theo ống cộng hưởng, giảm dần của nó the piston. As the pressure wave travels along the resonant tube, its descending
một phần (mặt trước của sóng) trở nên ngắn hơn trong khi một tăng dần (các part (the front of the wave) becomes shorter while the ascending one (the
đuôi của sóng) cấp độ tắt dần, cho cuối cùng là một dốc trước áp lực tail of the wave) levels off gradually, giving finally a steep pressure front
đặc trưng của một sóng xung kích. Các gradient cực cao của áp lực ở characteristic of a shock wave. The extremely high gradients of pressure at
mặt trước của máy bay sóng không chỉ bắt đầu tác động cơ học như chất lỏng the front of the plane wave not only initiate mechanical effects such as liquid
phân tán nhưng cũng có thể làm thay đổi tỷ lệ khô do tăng cường sự bốc hơi và dispersion but also can alter drying rates due to enhanced evaporation and
mao mạch dòng chảy của ẩm lỏng và hơi. capillary flow of liquid and vapor moisture.
Áp lực giống như, hồ sơ của pulsation vận tốc còn thực tế Unlike pressure, the profile of the velocity pulsation remains practically
không thay đổi dọc theo ống cộng hưởng và biến dạng của các vận tốc sin unchanged along the resonant tube and distortion of the sinusoidal velocity
pulsation chỉ xảy ra ở các ổ cắm ống. Như thể hiện trong hình 10.3, biên độ pulsation occurs only at the tube outlet. As shown in Figure 10.3, the amplitude
của vận tốc pulsation giảm mạnh với khoảng cách truyền sóng of velocity pulsation decreases sharply with the distance of wave propagation
trong không khí cởi mở. Để tận dụng đà của sóng xung kích, chất lỏng in open air. To take full advantage of the momentum of shock waves, liquid
được phân tán nên được cho ăn gần cửa thoát ra khỏi ống cộng hưởng, trong to be dispersed should be fed close to the outlet from the resonant tube, in
trường hợp này lên đến khoảng 20 cm. Ngoài ra, tác động mạnh của sóng xung kích do this case up to about 20 cm. Also, the strongest impact of shock wave due to
tốc độ không khí có thể được dự kiến trên một khoảng cách lên đến 1 m từ sự cộng hưởng air velocity might be expected over a distance up to 1 m from the resonance
ống. tube.
Hình đặc điểm 10,4 quà biên độ-tần số của hai khác nhau Figure 10.4 presents amplitude-frequency characteristics of two different
ống cộng hưởng, nơi mà các tần số cộng hưởng đầu tiên và thứ hai được rõ ràng resonant tubes, where the first and second resonance frequencies are clearly
xác định bởi cực đại liên tiếp trên các đường cong tương ứng. identified by the consecutive maxima on the respective curves.
Đối với một chiều dài ống được đưa ra, tần số cộng hưởng được tính như For a given tube length, the resonance frequency is calculated as
fr? (2n? 1) fr (2n 1)
v v
4Lt 4Lt
(10.1) (10.1)
trong đó v là vận tốc truyền sóng âm thanh, Lt là chiều dài ống, và n là where v is the velocity of sound propagation, Lt is the tube length, and n is
thứ tự của các tần số hài. the order of the harmonic frequency.
Từ phương. (10.1) nó sau đó các sản phẩm fr Lt không phụ thuộc vào From Eq. (10.1) it follows that the product fr Lt does not depend on the
đường kính ống mà là một đặc tính liên tục của môi trường dạng khí. tube diameter but is a constant characteristic of the gaseous environment.
Do đó, ở vận tốc âm thanh trong không khí bằng 330 m / s, cộng hưởng đầu tiên được Hence, at the sound velocity in air equal to 330 m/s, the first resonance is
lấy tại fr Lt ? 82,5 m / s. obtained at fr Lt 82.5 m/s.
134 Chương 10 134 Chapter 10
Hình 10.2 Đặc điểm của dao động áp lực trong ống cộng hưởng. FIGURE 10.2 Characteristic of pressure oscillation in the resonance tube.
Sấy với Waves Sốc 135 Drying with Shock Waves 135
Hình 10.3 Sự biến đổi của biên độ của vận tốc dao động với khoảng cách từ FIGURE 10.3 Variation of the amplitude of the pulsating velocity with distance from
đầu ra của ống cộng hưởng. the outlet of the resonance tube.
Biên độ tối đa của vận tốc pulsation xuất hiện ở n? 1 The maximum amplitude of the velocity pulsation appears at n 1
(Hình 10.4). Nó là khá hợp lý để giả định rằng biên độ của pulsation không khí (Figure 10.4). It is quite reasonable to assume that the amplitude of air pulsation
tại các ổ cắm ống là tỷ lệ thuận với biên độ của vận tốc của piston at the tube outlet is proportional to the amplitude of the velocity of piston
chuyển động movement
u? Kuc (10.2) u Kuc (10.2)
Kế toán các đường kính khác nhau của ống cộng hưởng (dt) và thay thế Accounting for the different diameters of the resonant tube (dt ) and substituting
(? Hợp lệ cho u 140 m / s) uc bởi (πfs), các phương trình sau đây đã được uc by (πfs), the following equation (valid for u 140 m/s) was
bắt nguồn bởi Lyulin (1998): derived by Lyulin (1998):
u? Zπfs u Zπfs
dc dc
dt dt
(10.3) (10.3)
trong đó s là độ dài đột quỵ piston, dc là đường kính piston, và Z là một hằng số where s is the piston stroke length, dc is the piston diameter, and Z is a constant
bằng 11,0 cho 0,044? dt? 0.005 m và bằng 9,1 cho 0.033? dt? equal to 11.0 for 0.044 dt 0.005 m and equal to 9.1 for 0.033 dt
0,044 m. Những giá trị này được xác định bằng thực nghiệm. 0.044 m. These values were determined experimentally.
136 Chương 10 136 Chapter 10
Hình 10.4 đặc tính cộng hưởng điển hình của các máy phát sóng xung kích. (Từ FIGURE 10.4 Typical resonance characteristics of the shock-wave generator. (From
Lyulin, 1998.) Lyulin, 1998.)
Thể hiện tần số trong điều khoản của trục khuỷu rpm, sau đây Expressing the frequency in terms of the crankshaft rpm, the following
tương quan thực nghiệm có thể được sử dụng để tính toán chiều dài của cộng hưởng experimental correlation can be used to calculate the length of the resonant
ống và biên độ vận tốc không khí tại các cửa hàng ống: tube and the amplitude of air velocity at the tube outlet:
u? u 0.0523ZsN dc
dt, m/s and Lt
15v
N
, m (10.4)
The shock wave acts as a liquid atomizer up to the point at which the
momentum of the shock wave is able to disperse the liquid stream. By analogy
with two-phase flow in packed columns, such hydrodynamic conditions can
be construed as ‘‘flooding.’’ Hence, the region of stable atomization is mapped
in terms of a flooding coefficient, defined as the mass flow ratio of undispersed
liquid to the total liquid subject to the shock-wave field
β
W Wd
W
(10.5)
Drying with Shock Waves 137
Lyulin (1998) provided the following empirical correlation for the flooding
coefficient:
β 1 A
ug
ul dt
dl2
(10.6)
where A is the constant, dl is the diameter of the liquid jet subject to atomization,
and ul and ug are the liquid jet velocity and the amplitude of the gas
velocity pulsation, respectively.
Thus, the generalized correlation for the flooding velocity shown in Figure
10.5 is
ul 0.00161 f 1.31 (ug 37.3)1/3
d0.25
l
(10.7)
where the liquid jet diameter dl is in mm, frequency f is in Hz, and the gas
velocity ug is in m/s.
The dispersion of pasty pigments with shock waves was studied experimentally
using the shock-wave generator with a resonance tube of 0.033 m.
This allows achieving air velocity equal to 163 m/s at 19.8 Hz of the reciprocating
movement of the piston. The pasty feed was located 0.05 m from the
resonance tube outlet at its axis. Such a distance was found to be optimal over
the range from 1.5 to 5 times the tube diameter.
The following procedure was used to obtain a droplet size distribution
(Muranov et al., 1997). Dispersed pigments were trapped in a filter paper
placed perpendicularly to the tube axis 1 m from the pasty feed. Segments of
the filter paper with spots of droplets were then analyzed under a microscope,
and about 2000 droplets were counted for the size distribution. Knowing the
dry mass of the dispersed pigment (m) and total surface area of the spots (SS ),
the volume of the droplet having (X, % wb) moisture content that leaves the
spot with diameter (dS ) can be calculated from
Vp
πd2S
4ρm
m
SS
100
100 X
(10.8)
where ρm is a density of the wet material.
Thus, the droplet diameter is
dp 6Vp
π 1/3
150d2S
m
SS(100 X)ρm1/3
(10.9)
FIGURE 10.5 Flooding curve for atomizing liquids with shock waves. (From Lyulin,
1998.)
Drying with Shock Waves 139
whereas the total surface area of dispersed liquid trapped in the filter paper
is
S n
i1
Sd,i n
i1
π(d2p
)i (10.10)
Typical distribution of droplet size for anticorrosive paint based on zinc
phosphate is shown in Figure 10.6. The symbol dM identifies here the median
diameter (midpoint of the size distribution) and dsV is the surface volume diameter,
i.e., diameter of the sphere having the same ratio of surface area-tovolume
as the droplet, and calculated as
dsV
Σd3i
ni
Σd2i
ni
(10.11)
Figure 10.6 indicates that droplets generated by the shock wave are
nearly monodispersed since the mass fraction of droplets larger than 27 μm is
negligible compared to the m
Một trong những công nghệ tiên tiến cho khâu nguyên tử hóa các chất lỏng nhớt và nhão mỏng One of the innovative technologies for atomizing viscous liquids and thin pasty
vật liệu trong một khí là việc sử dụng các sóng xung kích. Phương pháp này có thể được sử dụng trong materials in a gas is the use of shock waves. This method could be used in
sấy phun để giải tán các thức ăn lỏng (xem Chương 14) và do đó loại bỏ spray drying to disperse the liquid feed (see Chapter 14) and thus eliminate
phun thông thường từ hệ thống. Điều này sẽ tránh các vấn đề the conventional atomizer from the system. This will avoid problems with
xói mòn trong Atomizers đĩa và tắc nghẽn của các vòi phun đơn hoặc hai dòng. erosion in disk atomizers and clogging of single- or two-stream spray nozzles.
Ứng dụng tiềm năng của ý tưởng này trong các loại máy sấy vật liệu phân tán Potential applications of this idea in other types of dryers for dispersed materials
bao gồm khí nén, nhẫn, spin-flash và máy sấy xoáy, trong đó đà include pneumatic, ring, spin-flash, and vortex dryers, in which the momentum
của sóng xung kích có thể tăng cường tác động thủy động lực học của một quy ước of shock waves can enhance the hydrodynamic impact of a conventional
khí-carrier. gas-carrier.
Cần lưu ý rằng thuật ngữ '' sóng sốc '' là một áp lực It should be noted that the term ‘‘shock waves’’ refers to a pressure
sóng biên độ lớn nảy sinh từ các rối loạn sắc nét và bạo lực khi wave of large amplitude that arises from sharp and violent disturbances when
vận tốc truyền sóng vượt vận tốc của âm thanh lan truyền. the velocity of wave propagation exceeds the velocity of sound propagation.
Đặc trưng, một sự thay đổi đột ngột trong những tài sản trung bình (ví dụ, áp lực, Characteristically, an abrupt change of the medium properties (e.g., pressure,
căng thẳng, mật độ, vận tốc hạt, nhiệt độ, vv) diễn ra trong một giới hạn stress, density, particle velocity, temperature, etc.) takes place in a limited
không gian trên các sóng xung kích (Schetz và Fuhs, 1996; Shapiro, 1953; Anderson, space across the shock wave (Schetz and Fuhs, 1996; Shapiro, 1953; Anderson,
1982; Saad, 1992). Trong trường hợp được mô tả trong chương này, vật lý 1982; Saad, 1992). In the case described in this chapter, the physical
hiện tượng sóng xung kích được giới hạn cho một chiều truyền sóng máy bay, phenomenon of shock wave is restricted to one-dimensional plane wave propagation,
trong đó tính chất của không khí trong ống cộng hưởng của máy phát sóng in which properties of air in the resonant tube of the wave generator
131 131
132 Chương 10 132 Chapter 10
khác nhau đối với chỉ có một không gian phối hợp và thời gian. Mặc dù nó là kỹ thuật vary with respect to only one spatial coordinate and time. Although it is technically
khả thi để tạo ra một làn sóng sốc thật sự bằng cách di chuyển một piston vào một nén feasible to generate a true shock wave by moving a piston into a compressible
trung bình, vận tốc truyền sóng trong hệ thống được trình bày medium, the velocity of wave propagation in the system presented
ở đây là thấp hơn so với vận tốc âm thanh. Tuy nhiên, hồ sơ áp lực gần như bằng phẳng here is lower than the sonic velocity. However, the almost flat pressure profile
ở phía trước của sóng thoát khỏi máy phát điện là tương tự như một gần như liên tục at the front of the wave exiting the generator is similar to a nearly discontinuous
bị sốc trước tuyên truyền với vận tốc siêu âm. Vì không có đủ shock front propagating at a supersonic velocity. Because there is no adequate
định nghĩa cho các sóng áp suất của các đặc điểm như vậy, thuật ngữ '' sốc definition for the pressure wave of such characteristics, the term ‘‘shock
sóng '' sẽ được sử dụng trong suốt chương này. wave’’ will be used throughout this chapter.
Sương và sấy trong sóng xung kích vẫn đang ở giai đoạn phát triển, Atomization and drying in shock waves is still at the development stage,
ví dụ như, laboratory- và quy mô thí điểm thí nghiệm. Hình 10.1 trình bày sơ đồ e.g., laboratory- and pilot-scale experiments. Figure 10.1 presents schematically
máy phát điện giật sóng thử nghiệm được sử dụng bởi Lyulin (1998) để giải tán the experimental shock-wave generator used by Lyulin (1998) to disperse
các tài liệu nhão trong một Dyer phun. Các máy phát điện gồm một ống thép không gỉ pasty materials in a spray dyer. The generator consists of a stainless steel tube
0,04 m, đường kính, mà lan truyền sóng áp suất và phục vụ như là một 0.04 m in diameter, which propagates the pressure waves and serves as a
phần tư sóng (Helmholtz) cộng hưởng (xem Chương 14). Một đầu của sự cộng hưởng quarter-wave (Helmholtz) resonator (see Chapter 14). One end of the resonance
ống mở cửa để không khí trong khi khác được kết nối với một xung tube is open to the atmosphere while the other is connected to a pulse
máy phát điện thông qua một hình nón cụt dài 0,2 m. Các máy phát điện bao gồm một generator through a truncated cone 0.2 m long. The generator comprises a
buồng hình trụ 0,08 m, đường kính bên trong và một trục khuỷu-kết nối cylindrical chamber 0.08 m in internal diameter and a crankshaft-connecting
rod lắp ráp, trong đó di chuyển piston một cách qua lại. Các đột quỵ rod assembly, which moves the piston in a reciprocating manner. The stroke
của piston là 0,082 m. Máy phát xung được điều khiển bởi một 7-kW động cơ DC of the piston is 0.082 m. The pulse generator is driven by a 7-kW DC motor
với tốc độ quay cho phép kiểm soát tần số biến của các nét with controllable rotational speed allowing variable frequency of the strokes
7-28 Hz. from 7 to 28 Hz.
HÌNH 10.1 đồ của các máy phát điện giật sóng thử nghiệm. (Từ Lyulin, FIGURE 10.1 Schematic of the experimental shock-wave generator. (From Lyulin,
1998.) 1998.)
khô với Waves Sốc 133 Drying with Shock Waves 133
Áp lực và vận tốc tức thời phân bố dọc theo cộng hưởng The instantaneous pressure and velocity distributions along the resonance
ống được giám sát bởi các đầu dò áp điện và nhiệt nóng dây tube are monitored by piezoelectric transducers and hot-wire thermal
đo gió được kết nối với các dao động và hình ảnh ghi phim. anemometer that are connected to the oscilloscope and photo film recorder.
Những làm cho có thể điều chỉnh các máy phát điện để các cộng hưởng âm thanh bằng cách These make possible the tuning of the generator to the acoustic resonance by
thay đổi tốc độ quay của trục khuỷu. Ngoài ra, có một điều khoản để varying the rotational speed of the crankshaft. Also, there is a provision to
gắn ống cộng hưởng của chiều dài và đường kính khác nhau để có được yêu cầu attach resonance tubes of various lengths and diameters to obtain required
biên độ áp lực và vận tốc rung động. amplitudes of pressure and velocity pulsations.
Hình 10.2 trình bày một dao động áp lực thời gian điển hình tại nhiều Figure 10.2 presents a typical temporal pressure oscillation at various
điểm dọc theo ống cộng hưởng. Rõ ràng là hồ sơ cá nhân của dao động áp lực points along the resonance tube. It is clear that the profile of pressure oscillation
gần piston là hình sin vì sự chuyển động qua lại của near the piston is sinusoidal because of the reciprocating movement of
piston. Khi làn sóng áp lực di chuyển dọc theo ống cộng hưởng, giảm dần của nó the piston. As the pressure wave travels along the resonant tube, its descending
một phần (mặt trước của sóng) trở nên ngắn hơn trong khi một tăng dần (các part (the front of the wave) becomes shorter while the ascending one (the
đuôi của sóng) cấp độ tắt dần, cho cuối cùng là một dốc trước áp lực tail of the wave) levels off gradually, giving finally a steep pressure front
đặc trưng của một sóng xung kích. Các gradient cực cao của áp lực ở characteristic of a shock wave. The extremely high gradients of pressure at
mặt trước của máy bay sóng không chỉ bắt đầu tác động cơ học như chất lỏng the front of the plane wave not only initiate mechanical effects such as liquid
phân tán nhưng cũng có thể làm thay đổi tỷ lệ khô do tăng cường sự bốc hơi và dispersion but also can alter drying rates due to enhanced evaporation and
mao mạch dòng chảy của ẩm lỏng và hơi. capillary flow of liquid and vapor moisture.
Áp lực giống như, hồ sơ của pulsation vận tốc còn thực tế Unlike pressure, the profile of the velocity pulsation remains practically
không thay đổi dọc theo ống cộng hưởng và biến dạng của các vận tốc sin unchanged along the resonant tube and distortion of the sinusoidal velocity
pulsation chỉ xảy ra ở các ổ cắm ống. Như thể hiện trong hình 10.3, biên độ pulsation occurs only at the tube outlet. As shown in Figure 10.3, the amplitude
của vận tốc pulsation giảm mạnh với khoảng cách truyền sóng of velocity pulsation decreases sharply with the distance of wave propagation
trong không khí cởi mở. Để tận dụng đà của sóng xung kích, chất lỏng in open air. To take full advantage of the momentum of shock waves, liquid
được phân tán nên được cho ăn gần cửa thoát ra khỏi ống cộng hưởng, trong to be dispersed should be fed close to the outlet from the resonant tube, in
trường hợp này lên đến khoảng 20 cm. Ngoài ra, tác động mạnh của sóng xung kích do this case up to about 20 cm. Also, the strongest impact of shock wave due to
tốc độ không khí có thể được dự kiến trên một khoảng cách lên đến 1 m từ sự cộng hưởng air velocity might be expected over a distance up to 1 m from the resonance
ống. tube.
Hình đặc điểm 10,4 quà biên độ-tần số của hai khác nhau Figure 10.4 presents amplitude-frequency characteristics of two different
ống cộng hưởng, nơi mà các tần số cộng hưởng đầu tiên và thứ hai được rõ ràng resonant tubes, where the first and second resonance frequencies are clearly
xác định bởi cực đại liên tiếp trên các đường cong tương ứng. identified by the consecutive maxima on the respective curves.
Đối với một chiều dài ống được đưa ra, tần số cộng hưởng được tính như For a given tube length, the resonance frequency is calculated as
fr? (2n? 1) fr (2n 1)
v v
4Lt 4Lt
(10.1) (10.1)
trong đó v là vận tốc truyền sóng âm thanh, Lt là chiều dài ống, và n là where v is the velocity of sound propagation, Lt is the tube length, and n is
thứ tự của các tần số hài. the order of the harmonic frequency.
Từ phương. (10.1) nó sau đó các sản phẩm fr Lt không phụ thuộc vào From Eq. (10.1) it follows that the product fr Lt does not depend on the
đường kính ống mà là một đặc tính liên tục của môi trường dạng khí. tube diameter but is a constant characteristic of the gaseous environment.
Do đó, ở vận tốc âm thanh trong không khí bằng 330 m / s, cộng hưởng đầu tiên được Hence, at the sound velocity in air equal to 330 m/s, the first resonance is
lấy tại fr Lt ? 82,5 m / s. obtained at fr Lt 82.5 m/s.
134 Chương 10 134 Chapter 10
Hình 10.2 Đặc điểm của dao động áp lực trong ống cộng hưởng. FIGURE 10.2 Characteristic of pressure oscillation in the resonance tube.
Sấy với Waves Sốc 135 Drying with Shock Waves 135
Hình 10.3 Sự biến đổi của biên độ của vận tốc dao động với khoảng cách từ FIGURE 10.3 Variation of the amplitude of the pulsating velocity with distance from
đầu ra của ống cộng hưởng. the outlet of the resonance tube.
Biên độ tối đa của vận tốc pulsation xuất hiện ở n? 1 The maximum amplitude of the velocity pulsation appears at n 1
(Hình 10.4). Nó là khá hợp lý để giả định rằng biên độ của pulsation không khí (Figure 10.4). It is quite reasonable to assume that the amplitude of air pulsation
tại các ổ cắm ống là tỷ lệ thuận với biên độ của vận tốc của piston at the tube outlet is proportional to the amplitude of the velocity of piston
chuyển động movement
u? Kuc (10.2) u Kuc (10.2)
Kế toán các đường kính khác nhau của ống cộng hưởng (dt) và thay thế Accounting for the different diameters of the resonant tube (dt ) and substituting
(? Hợp lệ cho u 140 m / s) uc bởi (πfs), các phương trình sau đây đã được uc by (πfs), the following equation (valid for u 140 m/s) was
bắt nguồn bởi Lyulin (1998): derived by Lyulin (1998):
u? Zπfs u Zπfs
dc dc
dt dt
(10.3) (10.3)
trong đó s là độ dài đột quỵ piston, dc là đường kính piston, và Z là một hằng số where s is the piston stroke length, dc is the piston diameter, and Z is a constant
bằng 11,0 cho 0,044? dt? 0.005 m và bằng 9,1 cho 0.033? dt? equal to 11.0 for 0.044 dt 0.005 m and equal to 9.1 for 0.033 dt
0,044 m. Những giá trị này được xác định bằng thực nghiệm. 0.044 m. These values were determined experimentally.
136 Chương 10 136 Chapter 10
Hình 10.4 đặc tính cộng hưởng điển hình của các máy phát sóng xung kích. (Từ FIGURE 10.4 Typical resonance characteristics of the shock-wave generator. (From
Lyulin, 1998.) Lyulin, 1998.)
Thể hiện tần số trong điều khoản của trục khuỷu rpm, sau đây Expressing the frequency in terms of the crankshaft rpm, the following
tương quan thực nghiệm có thể được sử dụng để tính toán chiều dài của cộng hưởng experimental correlation can be used to calculate the length of the resonant
ống và biên độ vận tốc không khí tại các cửa hàng ống: tube and the amplitude of air velocity at the tube outlet:
u? u 0.0523ZsN dc
dt, m/s and Lt
15v
N
, m (10.4)
The shock wave acts as a liquid atomizer up to the point at which the
momentum of the shock wave is able to disperse the liquid stream. By analogy
with two-phase flow in packed columns, such hydrodynamic conditions can
be construed as ‘‘flooding.’’ Hence, the region of stable atomization is mapped
in terms of a flooding coefficient, defined as the mass flow ratio of undispersed
liquid to the total liquid subject to the shock-wave field
β
W Wd
W
(10.5)
Drying with Shock Waves 137
Lyulin (1998) provided the following empirical correlation for the flooding
coefficient:
β 1 A
ug
ul dt
dl2
(10.6)
where A is the constant, dl is the diameter of the liquid jet subject to atomization,
and ul and ug are the liquid jet velocity and the amplitude of the gas
velocity pulsation, respectively.
Thus, the generalized correlation for the flooding velocity shown in Figure
10.5 is
ul 0.00161 f 1.31 (ug 37.3)1/3
d0.25
l
(10.7)
where the liquid jet diameter dl is in mm, frequency f is in Hz, and the gas
velocity ug is in m/s.
The dispersion of pasty pigments with shock waves was studied experimentally
using the shock-wave generator with a resonance tube of 0.033 m.
This allows achieving air velocity equal to 163 m/s at 19.8 Hz of the reciprocating
movement of the piston. The pasty feed was located 0.05 m from the
resonance tube outlet at its axis. Such a distance was found to be optimal over
the range from 1.5 to 5 times the tube diameter.
The following procedure was used to obtain a droplet size distribution
(Muranov et al., 1997). Dispersed pigments were trapped in a filter paper
placed perpendicularly to the tube axis 1 m from the pasty feed. Segments of
the filter paper with spots of droplets were then analyzed under a microscope,
and about 2000 droplets were counted for the size distribution. Knowing the
dry mass of the dispersed pigment (m) and total surface area of the spots (SS ),
the volume of the droplet having (X, % wb) moisture content that leaves the
spot with diameter (dS ) can be calculated from
Vp
πd2S
4ρm
m
SS
100
100 X
(10.8)
where ρm is a density of the wet material.
Thus, the droplet diameter is
dp 6Vp
π 1/3
150d2S
m
SS(100 X)ρm1/3
(10.9)
FIGURE 10.5 Flooding curve for atomizing liquids with shock waves. (From Lyulin,
1998.)
Drying with Shock Waves 139
whereas the total surface area of dispersed liquid trapped in the filter paper
is
S n
i1
Sd,i n
i1
π(d2p
)i (10.10)
Typical distribution of droplet size for anticorrosive paint based on zinc
phosphate is shown in Figure 10.6. The symbol dM identifies here the median
diameter (midpoint of the size distribution) and dsV is the surface volume diameter,
i.e., diameter of the sphere having the same ratio of surface area-tovolume
as the droplet, and calculated as
dsV
Σd3i
ni
Σd2i
ni
(10.11)
Figure 10.6 indicates that droplets generated by the shock wave are
nearly monodispersed since the mass fraction of droplets larger than 27 μm is
negligible compared to the m
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