In this paper, we used a Venturi tube for generating hydrodynamic cavitation, and in order to obtain the optimum conditions for this to be used in chemical processes, the relationship between the aggressive intensity of the cavitation and the downstream pressure where the cavitation bubbles collapse was investigated. The acoustic power and the luminescence induced by the bubbles collapsing were investigated under various cavitating conditions, and the relationships between these and the cavitation number, which depends on the upstream pressure, the downstream pressure at the throat of the tube and the vapor pressure of the test water, was found. It was shown that the optimum downstream pressure, i.e., the pressure in the region where the bubbles collapse, increased the aggressive intensity by a factor of about 100 compared to atmospheric pressure without the need to increase the input power. Although the optimum downstream pressure varied with the upstream pressure, the cavitation number giving the optimum conditions was constant for all upstream pressures.

Cavitation can be used for chemical processes and/or water treatment. Chemical reactions caused by cavitation belong in the research area of sonochemistry, as cavitation is normally generated by ultrasonic vibrations. This sort of cavitation is called acoustic cavitation.1 In order to increase the intensity of acoustic cavitation, the effects of frequency, amplitude and the liquid used have been studied.2,3 On the other hand, high speed water flow through an orifice or Venturi tube also causes cavitation, and this phenomenon is called hydrodynamic cavitation.1 Research into enhancing the intensity of hydrodynamic cavitation has also been widely reported.

It has been shown that the formation of chemical products and the chemical luminescence induced by acoustic cavitation change with the gas used and the ambient pressure.4–7 Similarly, the luminescence induced by hydrodynamic cavitation also depends on the gas and ambient pressure.8 Furthermore, it has been reported that multibubble sonoluminescence induced by acoustic cavitation has a peak at a pressure lower than atmospheric9 and a theoretical study of the effect of the ambient pressure on the sonochemical reaction has also been reported.10 A system to generate acoustic cavitation at ambient pressures in excess of 30 MPa has been developed.11 However, some studies have reported that the intensity of hydrodynamic cavitation could be increased with less energy compared with that required for acoustic cavitation.12 In practical applications for chemical reactors, such as water treatment systems, hydrodynamic cavitation is preferable to acoustic cavitation, as it can be easily scaled up to enhance its aggressive intensity, and acoustic cavitation, moreover, has not been applied to large scale operations because of the difficulties in scaling up ultrasonic reactors. Hydrodynamic cavitation has been used for wastewater treatment, such as ballast water treatment, owing to its high efficiency compared with acoustic cavitation. Jawale et al. also reported that hydrodynamic cavitation reactors offer considerable promise in the treatment of cyanide containing wastewater because of the higher per unit energy of hydrodynamic cavitation.12 The Weissler reaction has been used for measuring the aggressive intensity of ultrasonic and hydrodynamic cavitation; however, it has been suggested that the Weissler reaction is not a good model for assessing the effectiveness of hydrodynamic cavitation.13 In a previous study, we showed that the luminescence intensity and the acoustic energy of hydrodynamic cavitation are related to the aggressive intensity.14 

In the case of hydrodynamic cavitation, in general, an increase in upstream pressure results in an increase in the aggressive intensity. Thus, greater input energy enhances the aggressive intensity. The maximum aggressive intensity for hydrodynamic cavitation using a cavitating jet through a nozzle occurs when the cavitation number, the ratio between the downstream and upstream pressures of the nozzle, is about 0.01.15,16 Therefore, the aggressive intensity for hydrodynamic cavitation can be increased by controlling the downstream pressure, i.e., the pressure in the region where the cavitation bubbles collapse. Thus, with a Venturi tube the aggressive intensity can be increased by controlling the pressure at the outlet to the tube. In practical applications, a valve downstream from the bubble collapsing region can increase the efficiency of the process without an increase in input power. This is an important advantage of using hydrodynamic cavitation. However, the optimum pressure for the region where the bubbles collapse is unknown.

In this paper, we demonstrate that the aggressive intensity of hydrodynamic cavitation through a Venturi tube can be increased by controlling the pressure where the bubbles collapse. In this investigation we varied the upstream pressure and the downstream pressure at the throat of the Venturi tube, and determined the optimum conditions. The aggressive intensity was estimated from the acoustic power, which was calculated from the acoustic pressure threshold and the number of acoustic pulses measured using a hydrophone. The luminescence was evaluated using a photoelectron multiplier.

Figure 1 shows a schematic illustration of the experimental apparatus for hydrodynamic cavitation using a Venturi tube. The test water is pressurized by a diaphragm pump and injected into the Venturi tube. The upstream pressure p1 and the downstream pressure p2 of the Venturi tube are measured by pressure gages and transducers. The upstream pressure, i.e., the injection pressure, is controlled by the rotational speed of the diaphragm pump. The downstream pressure is controlled using the downstream valve. Here, p1 and p2 are the absolute pressures. That is, when the downstream pressure is atmospheric pressure, p2 is 0.1 MPa. Water from an ion exchange system is used for the test water, which is kept at 290 ± 1 K. In order to eliminate residual bubbles after the cavitation bubbles have collapsed, the pipe from the Venturi tube goes into one tank (Tank B), while the pipe connected to the diaphragm pump comes from another tank (Tank A). Tanks A and B are connected by a pipe to equalize the water levels. Figure 2 shows the shape of the quartz Venturi tube used in the apparatus. The inner diameter D and the throat diameter d of the tube are 3.6 mm and 1.19 mm, respectively. The inner diameter gradually decreases from 3.6 mm to 1.19 mm over 20 mm, and then gradually increases from 1.19 mm to 3.6 mm over a further 20 mm as shown in Fig. 2.

The key parameter for cavitating flow is the cavitation number σ, which is defined by the following equation (1).

σ = p 2 p v 1 2 ρ U 2 = p 2 p v p 1 p 2 .
(1)

where pv is the vapor pressure of the test water, and U is the velocity at the throat.

The aggressive intensity of the cavitation bubbles collapsing was determined from the acoustic energy and the luminescence. The acoustic energy was estimated from the acoustic pulses received by a microphone with a range up to 100 kHz. The noise was analyzed by a pulse height analyzer through a 20 kHz high pass filter. The acoustic energy EA is proportional to the mass loss rate induced by cavitation erosion,8 and is calculated using the following procedure. The acoustic pulse propagates spherically,17 so the acoustic energy for an individual bubble collapsing, Ei, is determined from the following equation:

E i = P i 2 2 ρ C .
(2)

where Pi is the pressure, ρ is the density, and C is the acoustic speed. The acoustic energy per unit time, EA, is defined by the sum of the squares of the acoustic pressure Pi, where the pressure pulse is larger than a threshold level, Pth, as follows,

E A = E i Δ t = k P th P i 2 Δ t .
(3)

In this paper, Δt = 1, P th P i 2 so , which is equal to EA/k, is used for the acoustic energy.

The luminescence intensity was evaluated using a luminescence analyzer. The test section was set in the test chamber in the analyzer. The photomultiplier tube in the analyzer can detect 50 - 108 photons/cm2/s. 1 count of the analyzer is equivalent to 50 photons. The luminescence spectrum was evaluated using high-pass filters with the analyzer.

In order to investigate the behavior in the cavitating region, the cavitating flow was observed using a high-speed video camera, with a maximum frame rate of 100000 frames per second. A Xenon flash lamp with an exposure time of 1.1 μs was used to enable instantaneous pictures of the cavitating flow to be taken.

The cavitating region in the Venturi tube was observed with the high-speed video camera to illustrate how the appearance of the cavitating flow changes with time. This is shown in Fig. 3. The injection pressure p1 was 0.6 MPa and the downstream pressure p2 was 0.12 MPa. The frame rate of the video camera during recording was 20000 frames per seconds. The white region shows the cavitating region. The bubbles coming through the Venturi tube form a kind of cavitation cloud consisting of many small bubbles. The size of the cavitating region increases with time, and then falls back slightly at t = 0.25 ms, increases again, then falls back again. Thus, the cavitating region changes with time with the cavitation cloud shedding periodically, the same as for a cavitating jet.18 

Figure 4 illustrates the effect on the cavitating region of changing the upstream pressure p1 at constant downstream pressure (p2 = 0.12 MPa). As shown in Fig. 3, the length of the cavitation region changes with time, and the longest region was chosen for Fig. 4. The length of the cavitation region increases monotonously with increasing upstream pressure p1 at constant downstream pressure. Increasing the upstream pressure increases the pressure difference, thereby decreasing the cavitation number. For example, σ is about 0.42 with p1 = 0.4 MPa and p2 = 0.12 MPa and about 0.24 with p1 = 0.6 MPa and p2 = 0.12 MPa. Thus, the cavitation develops further when the cavitation number is smaller.

Figure 5 shows the effect on the cavitating region of changing the downstream pressure p2 at constant upstream pressure (p1 = 0.6 MPa). As shown in Fig. 4, the longest cavitating region was chosen for each condition. As shown in Fig. 5, when p1 is constant, the cavitating length decreases with increasing p2, as the pressure difference between p1 and p2 decreases.

In order to investigate the effect of the downstream pressure on the aggressive intensity produced by the bubbles collapsing, the acoustic energy EA was plotted as a function of the downstream pressure p2. These plots, with various upstream pressures and the threshold level pth varying from 0.5 to 2.0 kPa, are shown in Fig. 6. At relatively low threshold levels, such as at 0.5 and 1.0 kPa, EA decreases as p2 increases from 0.12 MPa to 0.14 MPa, after which, it increases and reaches a maximum, before decreasing again. The downstream pressure where EA reaches its maximum is the optimum downstream pressure, denoted as p2 opt. For example, with p1 = 0.60 MPa and pth = 0.5 kPa, EA is 3.3 × 109 Pa2/s with p2 = 0.12 MPa and 1.2 × 1010 Pa2/s with p2 = p2 opt, which is 0.23 MPa. Moreover, with p1 = 0.60 MPa and pth = 1.5 kPa, EA is 2.7 × 106 Pa2/s at p2 = 0.12 MPa and 2.7 × 108 Pa2/s at p2 = p2 opt, again 0.23 MPa. Comparison of EA at p2 = 0.12 MPa and p2 opt = 0.23 MPa shows increases of 3.6 for pth = 0.5 kPa and 100 for pth = 1.5 kPa, demonstrating that the acoustic power can be increased by increasing p2. Thus, increasing the downstream pressure in the region where the bubbles collapse increases the aggressive intensity of the cavitation. The optimum downstream pressure increases with increasing p1. The values of p2 opt with p1 = 0.40, 0.45, 0.50, 0.55 and 0.60 MPa are 0.16, 0.17, 0.18, 0.21 and 0.23 MPa, respectively.

As the pressure in the region where the bubbles collapse can be increased by opening the downstream valve, the aggressive intensity of the cavitation can be boosted by optimizing the downstream pressure without the need for additional power. The reason why the acoustic energy EA has a maximum is considered to be as follows. The bubbles shrink and re-expand with a velocity that increases with increasing downstream pressure. The cavitation number σ also increases with downstream pressure. It is assumed that the pressure of the collapsing field of the cavitation bubbles increases with the increases in p2 and σ. As a result, the impact energy generated by individual bubbles increase. In other words, the stronger bubble-bubble interaction is occurred at lower cavitation number as more bubbles are formed at smaller cavitation number, and the interaction reduces the acoustic energy as well as luminescence intensity.19,20 On the other hand, as the cavitating region shrinks with increasing p2 and σ, the number of cavitation impacts is reduced. For this reason, it is believed that the acoustic power EA has a maximum.

The effect of the upstream pressure p1 on the optimum downstream pressure p2 opt can be seen in Fig. 7(a) which shows the relationship between the acoustic energy EA and the downstream pressure p2 at various upstream pressures. The data for Fig. 7(a) was chosen from the data with pth = 1 kPa in Fig. 6. As mentioned above, the acoustic power EA has a maximum at a particular downstream pressure, i.e., p2 opt. The optimum downstream pressure increases with increasing p1. In order to investigate the effect of the cavitation number on the relationship between p1 and p2 opt, the relationship between EA and the cavitation number σ at various upstream pressures is plotted in Fig. 7(b). As shown in Fig. 7(b), EA has a maximum at around σ = 0.6 regardless of p1. The cavitation number at which EA has a maximum is the optimum cavitation number and is denoted as σopt. Thus, it can be concluded that the value of σ at which EA has a maximum is constant.

Next, we investigated the effect of the downstream pressure p2 and the cavitation number σ on the bubble temperature and the number of active bubbles of the hydrodynamic cavitation. Figure 8(a) illustrates the relationship between the luminescence intensity CL and the downstream pressure p2 at various upstream pressures. The luminescence intensity CL has a maximum with respect to the downstream pressure, and the behavior is similar to that in Fig. 7(a). Figure 8(b) illustrates the relationship between CL and the cavitation number σ at various p1. As shown in Fig. 8(b), CL has a maximum at an almost constant value of σ (≈ 0.4), similar to Fig. 7(b).

In Figs. 9 and 10, comparisons between the optimum acoustic energy EA at pth = 1.0 kPa and the luminescence intensity CL are made. In Fig. 9, for each of these, the optimum downstream pressure is plotted against p1, while in Fig. 10, the optimum cavitation number, σopt, is plotted against p1. As shown in Fig. 9, p2 opt of EA and CL both increase with increasing p1. On the other hand, in Fig. 10, σopt has almost constant values. As mentioned above, the main parameter for cavitating flow is the cavitation number. The value of σopt for CL is much smaller than that for EA. Let’s think about the reason for this. In a previous report with regard to luminescence spots induced by a cavitating jet measured by an EM-CCD camera, σopt at a low luminescence threshold level was smaller than that at a high threshold level.8 This result suggests that the luminescence measured by the luminescence analyzer gave a smaller aggressive intensity, as the analyzer uses a photomultiplier for the measurement.

Figure 11 shows the relationship between the maximum acoustic energy EAmax, i.e., at EA at p2 opt, and the upstream pressure p1. As shown in Fig. 11, the relationship follows a power law. For example, in the case of pth = 0.5 kPa, the exponent in this power law is 11.6. Figure 12 illustrates the relationship between the maximum luminescence intensity, CLmax, i.e., CL at p2 opt, and p1. The maximum luminescence intensity CLmax is proportional to a power of the upstream pressure p1 in the same way as in Fig. 11. These tendencies suggest that the aggressive intensity of hydrodynamic cavitation can be increased by increasing the injection pressure, although an increase in input power is required. Note that the optimum downstream pressure, i.e., the pressure where the bubbles collapse, should be considered.

Figure 13 shows the results of spectroanalysis of the luminescence at various downstream pressures and constant upstream pressures of 0.40 and 0.60 MPa. As shown in Fig. 13, the luminescence intensity CL has maxima at λ = 350 and 440 nm. According to Sehgal et al.21 and K. Yasui et al.,22 the hydroxyl radical induced by acoustic cavitation produces luminescence at relatively short wavelengths, such as 310 nm. In one of our previous reports,14 we used a spin trapping method utilizing the electron spin resonance of the hydrodynamic cavitation induced by a cavitating jet to reveal a similar result to that for acoustic cavitation. Thus, it appears that the source of the luminescence induced by the hydrodynamic cavitation through a Venturi tube are hydroxyl radicals, the same as in acoustic cavitation. Thus, it can be concluded that hydrodynamic cavitation, as well as acoustic cavitation, produces hydroxyl radicals. Actually, the quartz of Venturi tube might reduce the intensity of luminescence at short wavelength. The plasma inside bubble also generates luminescence at various wavelengths.22 These are the reasons why the luminescence intensity CL has maxima at λ = 350 and 440 nm.

In order to find suitable conditions for hydrodynamic cavitation for practical applications, the aggressive intensity of the hydrodynamic cavitation produced in a Venturi tube was investigated. The aggressive intensity at various upstream and downstream pressures, and consequently various values of the cavitation number, was estimated. The aggressive intensity was estimated from the acoustic power calculated from the acoustic pressure threshold pth and the number of acoustic pulses measured by a hydrophone. The luminescence was also evaluated using a photoelectron multiplier. The main results obtained are summarized as follows:

  1. The aggressive intensity varied with the downstream pressure applied in the region where the cavitation bubbles collapse, and had a maximum at a particular downstream pressure. This means that the aggressive intensity can be simply increased by controlling a valve on the downstream side without the need for additional power. For example, in the case of p1 = 0.6 MPa and pth = 1.5 kPa, the acoustic power with p2 = 0.23 MPa is about 100 times greater than that with p2 = 0.12 MPa.

  2. Although the downstream pressure at which the maximum aggressive intensity occurred varied with the upstream pressure, the cavitation number for this condition was constant.

  3. The length of the cavitating region in the Venturi tube changed with time. Although the maximum and the time averaged length of the cavitating region decreased monotonously with increasing cavitation number, the aggressive intensity had a maximum at a particular cavitation number.

  4. When hydrodynamic cavitation is generated using a Venturi tube, the luminescence can be measured by a photoelectron multiplier at relatively low injection pressures, such as 0.4 MPa absolute pressure, i.e., 0.3 MPa relative pressure.

This work was partly supported by the Japan Society for the Promotion of Science under Grant-in-aid for Scientific Research (B) 24360040 and The Canon Foundation. The author thanks Mr. M. Mikami, Technician of the Department of Nanomechanics and Mr. T. Muraoka, ex-student of the Graduate School of Engineering, Tohoku University for their help in the experiments.

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