Kai Zhang (張凱), Zhi-yong Dong (董志勇), Rui-hao Yao (姚銳豪)

Research Institute of Hydraulic and Municipal Engineering, Zhejiang University of Technology, Hangzhou 310014, China

Introduction

Hydrodynamic cavitation is a novel technique that has substantial application in wastewater treatment, especially in degradation of refractory pollutants. Cavitation means phenomena of formation,growth and collapse of cavitation bubbles. Microjets and shock waves due to collapse of cavitation bubbles can release high intensity energy, which generate strong oxidation conditions of chemical process such as hydroxyl radical and hydrogen peroxide[1-2]. Pandit and Joshi[3] first applied hydrodynamic cavitation on wastewater treatment. As research continued, it was found that keeping the other conditions consistent, the geometric size of cavitation device was the major factor to directly determine cavitation effect and cavitation characteristics in bulk liquid, and played a critical role in effective wastewater treatment. Siva Kummar et al.[4]experimentally investigated the degradation of rhodamine B samples using six different geometric configurations of circular multiorifice plates and reported that the size of orifice influenced the degradation rates of aromatic amines.Vichare et al.[5]have conducted experiments on the decomposition of aqueous KI by hydrodynamic cavitation, and found that by optimizing the geometry of the cavitation device, the decomposition rate of KI would increase by 3-5 times. Some researchers utilized hydrodynamic cavitation to degrade wastewater, and made a certain progress, but the hydrodynamic cavitation reactors did not reach the good effects. They had to unite with the other advanced oxidation process (AOP), for example, Fenton oxidation, ferric ion catalysis and photocatalysis etc., to increase the treatment effect of hydrodynamic cavitation reactor[6-9]. Wu et al.[10], Wang and Zhang[11]experimentally investigated dynamic characteristics of degradation of chlorocarbon and alachlor by hydrodynamic cavitation. Yang et al.[12]and Bing et al.[13]respectively studied the cavitational characteristics induced by triangular and square multi-orifice plates and their results showed that the open-porosity of multi-orifice plates significantly influenced cavitation number and hence affected the cavitation intensity based on the degradation experiments of p-nitrophenol.Dong et al.[14], Zhang[15], Xiao[16]investigated the degradation of p-nitrophenol and nitrobenzene mixtures by using the combination of the Venturi tube with multi-orifice plates. They reported that the number, size and arrangement of orifice and the combination orders directly affected the extent of degradation. In addition, Chen et al.[17], Yang et al.[18]performed numerical simulation in the cavitation characteristics of square and triangular multi-orifice plates, and the numerical simulation results were verified by 3-D PIV and high-speed motion picture camera. Han et al.[19]studied the pressure characteristics of multi-orifice plates aimed to reveal the mechanism of removal of refractory pollutants due to multi-orifice plate. However, study of pressure characteristics in combination cavitation reactors has not been reported before.

When high-speed liquid passed through the throat of Venturi tube, the flow velocity increased sharply and the pressure dropped rapidly. There existed a low-pressure region in throat, where cavities were formed and grown. High-speed flow through multi-orifice plates would turn to be multiple turbulent jets which are mixing and shearing with each other and hence resulting in the pressure fluctuation in cavitation region. In order to reveal the pressure characteristics of cavitation flow field, time-averaged pressure, cavitation number, pressure frequency spectrum and auto-correlation function in the throat of Venturi tube and behind multi-orifice plates were measured based on the self-developed hydrodynamic cavitation reactors composed of the Venturi tubes,triangular multi-orifice plates and their combinations.The effects of throat length, different numbers, sizes and arrangements of orifice, and the combination categories of Venturi tubes with multi-orifice plates on pressure characteristics have been analyzed in detail.

1. Experimental facility and measuring method

1.1 Experimental facility

The experimental apparatus was shown in Fig. 1.

Three types of Venturi tubes based on different throat length (L/R, whereLis throat length,Ris hydraulic radius) were designed in the experiment:L/R= 20, 40 and 60. The distribution of measuring points was shown in Fig. 2. The location parameters of measuring points was listed in Table 1, and the inlet of contraction section was defined as origin of coordinates.

There were five measuring points on the bottom of working section and a pressure gauge was installed in front of plate. The distribution of measuring points was shown in Fig. 3. The location parameters of measuring points was listed in Table 2, the position where multi-orifice plates existed was defined as origin of coordinates. Four types of triangular orifices plates were designed in the experiment(Fig. 4). The parameters of the multi-orifice plates were shown in Table 3.

Fig. 1 Schematic of the experimental apparatus

Fig. 2 (Color online) Location of measuring points of the Venturi tube 2

Fig. 3 (Color online)Locationof measuring pointsbehind multi-orifice plates

Fig. 4 Triangular multi-orifice plates

The combination setup was shown in Fig. 5, the flow from the Venturi tube to the multi-orifice plate.

Table 1 Location parameters of measuring points of the Venturi tube 2

Table 2 Location parameters of measuring points behind multi-orifice plates

Table 3 Geometric characteristics of multi-orifice plates

Fig.5 (Color online) Combination of Venturi tube with triangular multi-orifice plate

1.2 Measuring method

Pressure data were collected and analyzed by the SINOCERA-YE6263 data acquisition system. The acquired data were the flow transient pressurep,which could be expressed as the sum of time-averaged valueand fluctuating valuep′, that is

The signal of fluctuating pressure could be converted from time domain to frequency domain by an analysis of power spectrum. The power spectral density function is obtained by performing a fast Fourier transform based on pressure data wherekis frequency order corresponding to power spectrum,Nthe sampling number, Δttime interval, Δt=0.001 was adopted in this paper.

The degree of similarity between pressure signal and inhibit signal is determined quantitatively by auto-correlation function, which reflects the periodicity of fluctuating pressure. According to statistical theory, auto-correlation function of fluctuating pressure is defined as

2. Results and discussions

2.1 Time-averaged pressure analysis

2.1.1 Time-averaged pressure behind multi-orifice

plates

Figure 6 showed the distribution of time-averaged pressures behind triangular multi-orifice plates.As can be seen from Fig. 6, flow pressure dropped to negative value behind multi-orifice plates and cavitation bubbles formed, as an abruptly rising in pressure later, bubbles collapsed suddenly, thus being helpful to promote hydroxyl radicals to enter into liquid phase as early as possible and react with hydrophilic pollutants. Then pressure tended to be stable after the measuring point 2. It can be attributed that, as to the decrease in cross-sectional area when flow through the multi-orifice plates, these was a rapid increase in flow velocity. Due to the faster flow velocity, high speed jet produced, and resulted in a drop decrease in flow pressure, then flow pressure rose rapidly as a result of the expand of cross-sectional area as well as the extend of jets, and the pressure gradually tended to be stable finally. As shown in Fig. 6, the pressure fluctuation induced by plates 1 and 4 was on a scale from 300 kPa to 500 kPa, while that exceeded 500 kPa induced by plate 2 and 3. This indicated that when flow passed through multi-orifice plate, the pressure magnitude increased and the strong variation in pressure occurred with an increase in the number of orifice based on the same size of orifice. In addition,by comparison of plates 2 and 4 it could be concluded that the pressure fluctuation due to bigger size of orifice was greater than the smaller one.

2.1.2 Time-averaged pressure in the throat of Venturi tubes

Figure 7 showed the distribution of time-averaged pressures in the throat of the Venturi tube 2 under two velocities condition. It followed that the pressure in throat decreased to negative value when flowing through the contraction section, and it remained negative pressure condition. With the flow continually passed through the diffusion section, the pressure recovered. Moreover, the Venturi tube 2 with longer throat length could extend the duration time of negative pressure, which could let bubble to expand and be helpful to hydrophobic pollutants for entering into bubble to be pyrolyzed with the bubble collapsed.

Fig.6 Time-averaged pressures behind multi-orifice plates

Fig.7 Time-averaged pressures in the throat of the Venturi tube 2

Fig.8 Time-averaged pressures in the throats of combination forms

2.1.3 Time-averaged pressure due to the combination of Venturi tubes with multi-orifice plates

In the forms of combination of the Venturi tube 2 with multi-orifice plates, time-averaged pressures in the throat of Venturi tube affected by multi-orifice plates in the downstream were shown in Fig. 8. It showed that the variation of pressures in throat was in accordance with Fig. 6, namely, it decreased sharply first, and then remained low value. Increasing throat length could extend the duration time of bubbles in throat, and make for bubble to grow, which ensure the cavitation action in the Venturi tube.

Figure 9 showed the pressure distribution behind the multi-orifice plate 1 which was affected by the Venturi tube in upstream location. As shown here,there was a sudden drop in flow pressure behind multi-orifice plates at first, and then the pressure has a slight increased, it continually tended to be stable after the measuring point 2, and this phenomenon benefited for bubbles producing and collapsing. Connection with Fig. 7, the throat of Venturi tube in upstream location could obviously promote the decreasing in pressure as well as intensify the fluctuating in pressure of multi-orifice plates, and that also restrained the recovery of pressure in downstream.

Fig.9 Time-averaged pressures behind the multi-orifice plate 1 of combination forms

2.2 Cavitation number analysis

The cavitation number is essentially a pressure coefficient or an Euler number, represents the degree of flow cavitation, and reflects the effect of pressure variation on the flow characteristics, which can be expressed as

wherepis an absolute pressure of the measuring point,vpthe saturated vapor pressure, ρthe density of liquid,0Vthe velocity of liquid. Figure 10 (a)described the variation of cavitation number with distance in the forms of combination of the Venturi tube 2 with multi-orifice plates, that was, cavitation number generated behind multi-orifice plates was less than that in the throat of Venturi tube, thus suggesting that the cavitation phenomenon behind multi-orifice plates was more significant and the cavitation reaction was more turbulent. Figure 10 (b) gave the distribution of cavitation number induced only by the multi-orifice plates, it followed that after the measuring point 2, cavitation number has reached 0.3,and the maximum even exceeded 1.4, while it was basically stabilizing about 0.3 in the combination forms. This can be attributed that setting the Venturi tube upstream multi-orifice plates could extend the duration time of the lowest pressure and expansion period of cavitation bubble, and lead to enhancing the cavitation effect induced by multi-orifice plates.Consequently, the combination reactors provided an optimal hydraulic condition for the formation, growth and collapse of cavitation bubbles.

Fig.10 Variation in cavitation number

2.3 The spectrum characteristics of fluctuating pressure in combination reactors

Pressure fluctuation produces different frequency and scale of vortex in part of flow field, while the spectrum of fluctuating pressure reflects the distribution of fluctuation energy in frequency domain. In this part, combination reactors composed of Venturi tubes and multi-orifice plates were chosen as the analysis objects, the effect of relative throat length of Venturi tube, orifice number and size of multi-orifice plates on the power spectrum were investigated.

2.3.1 Effect of throat length on the power spectrum of fluctuating pressure

The measuring point 2 in throat were chosen as the experimental analysis object, Fig. 11 showed the variation of power spectrum of fluctuating pressure due to the Venturi tube 2. It followed that the power spectrums of fluctuating pressure exhibited a random white noise as a whole. The reason was that the throat with a certain length could extend the duration time of the minimum pressure in flow, and reduce the turbulence intensity in internal flow field. It was noteworthy that the band of fluctuation energy has a broaden tendency, which indicated that the throat length being ofL/R= 40 made for improving the fluctuation energy and promoting the energy distribute uniformly.

Fig.11 Effect of relative throat length on the power spectrum

2.3.2 Effect of orifice number on the power spectrum of fluctuating pressure

The variation of power spectrum of fluctuating pressure affected by orifice number was shown in Fig.12. The pressure data collected in the measuring point 1 were chosen as the analysis object. As shown here,based on the same size of orifice, the power spectrum of fluctuating pressure increased with an increase in the number of orifice, the dominant frequency was more obvious and the fluctuation energy increased as well. Moreover, the band of fluctuation showed a widen tendency, thus indicating that increasing the number of orifice could promote the uniformity of fluctuation energy in frequency domain. This could be explained that the spacing among multijet being smaller as a result of the more number of orifice, due to the smaller spacing, stronger mixing and entrainment among the jets resulted in the low frequency and large scale of vortexes translating into being of the high frequency and the small scale ones, as well as an increase in dominant frequency and power spectrum.A decrease in the scale of vortex could lead to smaller scale of vortexes produced in internal flow field, and hence promoting the distribution uniformity of fluctuating energy.

2.3.3 Effect of orifice size on the power spectrum of fluctuating pressure

The pressure data collected in the measuring

Fig.12 Effect of orifice number on the power spectrum

Fig.13 Effect of orifice size on the power spectrum

point 1 behind multi-orifice plates were taken for an example. A comparison of power spectrums induced by different multi-orifice plates with the same orifice number but of different size was shown in Fig. 13.Due to the bigger size of orifice, the dominant frequency was more obvious and the fluctuation energy concentrated on the band of low-frequency while the power spectrum of fluctuating pressure induced by the smaller one was a wide-band and showed a random white noise. The amplitude of power spectrum was uniform, and the fluctuation energy was greater. This could be attributed that the space among multijet became smaller and the role of mixing and entrainment was stronger based on the greater size of orifice,which resulted in a greater fluctuation energy, while in the case of smaller orifices, multi-jet could remain their own characteristics in a long distance behind multi-orifice plates (aboutL/R= 172 downstream),and reduce the pulsing of jets induced by entrainment and interfere, as well as accelerating the uniform distribution of fluctuation energy in frequency domain.

Fig.14 Auto-correlation of fluctuating pressure

2.4 Auto-correlation function of fluctuating pressure

As mentioned above, in combination reactors,both the pressure fluctuation and cavitation phenomenon behind the multi-orifice plate were most significant. The measuring point 2 behind multiorifice plate of the combination form in Fig. 5 was chosen to analyze the auto-correlation function of fluctuating pressure with and without plate, which was shown in Fig. 14. It was obvious that in both cases,the fluctuation pressure existed is periodic. In the case of combination contained a multi-orifice plate, the period of fluctuating pressure was extremely short,and there was two cycles each second averagely as shown in Fig. 14(a), while in the case that without multi-orifice plate, an average cycle was about 0.3 s as shown in Fig. 14(b). In addition, the amplitude in Fig.14(a) showed a great fluctuation, and the amplitude increased in the end and then obviously decreased,while it remained fairly consistent in Fig. 14(b), and showed significantly periodic as well as a good interrelation. In conclusion, multi-orifice plate could disturb the correlation of fluctuating pressure and result in reducing the period of fluctuation pressure,thus intensifying the fluctuation in flow pressure and hence producing the intense fluctuation energy.

3. Conclusions

Through the experimental and numerical study on the characteristics of time-averaged pressure, pressure frequency spectrum and auto-correlation function of pressure in the throats of Venturi tubes and behind multi-orifice plates, the following conclusions can be reached.

(1) When flow passed through the triangular multi-orifice plate, the flow pressure dropped to negative value and cavitation bubbles formed, as an abruptly rising in pressure later, bubbles collapsed suddenly, thus being helpful to promote hydroxyl radical to enter into liquid phase as early as possible and react with hydrophilic pollutants. Base on the same size of orifice, the pressure magnitude increased and the strong variation in pressure occurred with an increase in the number of orifice, leading to producing a great deal of cavitation bubble cluster. Furthermore,the pressure fluctuation due to bigger size of multiorifice plate was greater than the smaller one.

(2) Pressure in the throat decreased to negative value when flow through the contraction section of Venturi tube, and it could remain negative condition.Increasing the length of throat could extend the duration time of negative pressure, which could led bubble to expand and be helpful to hydrophobic pollutants for entering into bubble to be pyrolyzed with the bubble collapse.

(3) In the combination reactor, the cavitation number generated behind multi-orifice plates was less than that in the throat of Venturi tubes. The combination reactors provided an optimal hydraulic condition for the formation, growth and collapse of cavitation bubbles and made for degrading hydrophilic and hydrophobic pollutants synthetically.

(4) The power spectrums of fluctuating pressure in throat exhibited a random white noise as a whole.The band of fluctuation energy induced due to the throat, which was ofL/R= 40, has a broaden tendency. It made for improving the fluctuation energy and promoting the uniform energy distribution.Moreover, both increasing the number of orifice and decreasing the size of orifice could accelerate the uniform distribution of the fluctuation energy in frequency domain.

(5) In the combination reactor, the fluctuation of correlation function behind multi-orifice plate was more intense and the multi-orifice plate could reduce the cycle of fluctuation pressure and improve the fluctuation energy.

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