476 CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 26, No. 3, 2013 DOI: 10.3901/CJME.2013.03.476, available online at www.springerlink.com; www.cjmenet.com; www.cjmenet.com.cn Effect of Geometrical Parameters on Submerged Cavitation Jet Discharged YANG Minguan, XIAO Shengnan*, KANG Can, and WANG Yuli School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, China Received April 7, 2012; revised January 4, 2013; accepted February 25, 2013 Abstract: The flow characteristics of cavitation jets are essential issues among relevant studies. The physical properties of the jet are largely determined by the geometrical parameters of the nozzle. The structure and cavitation jets characteristics of the angular-nozzle and the self-resonating cavitation nozzle have been extensively studied, but little research is conducted in the central-body cavitation nozzle mainly because of its hard processing and the cavitation jet effect not satisfactory. In this paper, a novel central-body nozzle (a non-plunger central-body nozzle with square outlet) is studied to solve above problems. Submerged jets discharged from the novel central-body nozzle are simulated, employing the full cavitation model. The impact of nozzle configuration on jet properties is analyzed. The analysis results indicate that when central-body relative diameter keeps constant, there is an optimal contraction degree of nozzle s outlet, which can induce intense cavitation in the jet. The central-body relative diameter also affects jet profiles. In the case of large central-body relative diameter, most of the bubbles settle in the jet core. On the contrary, a smaller relative diameter makes bubbles concentrate in the interface between the jet and its surrounding fluid. Moreover, the shorter outlet part allows the cavitation zone further extend in both the axial and racial directions. The research results further consummate the study on the central-body nozzles and the correlation between cavitation jet and the structure, and elementarily reveal the mechanism of cavitation jet produced in a non-plunger novel central-body nozzle and the effect of the structure parameters on the cavitation jet, moreover, provide the theoretical basis for the optimal design of the nozzle. Key words: central-body nozzle, cavitation jet, square-outlet, numerical simulation 1 Introduction Cavitation erosion has a strong destructive power, which is used for cutting, cleaning, mining in varies of Engineering fields [1 4]. Cavitating jets which generate many bubbles in the jet beam use the energy emitted by bubbles collapse to increase the impact force of the jet. Many experiments and numerical calculations have been carried out by scholars to the cavitation jet. In the 80s of 20th century, the American researchers JOHNSON, et al [5], presented the concept of the self-resonating cavitation jet and carried out extensive research. From 1984, SHEN, et al [6 8], from China University of Petroleum began to study the self-oscillating cavitation jet and established a theory of self-oscillating cavitation nozzle design patterns after years of hard work; LIAO, et al [9 10], generated the cavitation jet theory of the self-excited oscillation pulsed nozzle; ERDMANN-JESNITZER, et al [11], studied the effect of the angular-nozzle structure dimensions on the submerged cavitation erosion; The Japanese scholar KATSUYA [12] investigated the impact of the diffuser section s shape of Corresponding author. E-mail: xsn1986@126.com This project is supported by National Natural Science Foundation of China (Grant No. 50806031) Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2013 the angular-nozzle on the cavitation jet in 1985. In the present literature the self-resonating cavitation nozzle and the angular cavitation nozzle are investigated a lot, however, the study of center-body cavitation nozzle is rarely reported. In the early research of center-body cavitation nozzle, JOHNSON, et al [13], proposed the concept of center-body nozzle; In Hydronauties Corporation, CONN, et al [14], invented two types of cavitation nozzles in 1968. One was the rotating blade cavitation nozzle, and the other was the plunger central-body nozzle. In 1974, MAURER [15] researched the influence of structure parameters on cavitation jet discharged from the central-body nozzle, who found that the highest efficiency came up when the central-body from the nozzle end face 3 mm and the optimum spray distance increased with the length of the nozzle pipe shorten. After this research the central-body nozzle was less concerned. Until 2009, LIU [16] from China University of Petroleum launched the experiments and simulations to research the impact of structure parameters and hydraulic parameters on cavitation jet discharged from central-body nozzle and the structure of the central-body nozzle was optimized according to the results. In 2010 the energy characteristics and the flow structure of free jet flow discharged from the central-body nozzle was studied by YANG, et al [17] from Jiangsu University, in order to
CHINESE JOURNAL OF MECHANICAL ENGINEERING 477 estimate the nozzle wear. The above investigations are all focused on the plunger central-body nozzle. The study in plunger central-body nozzle is less popular because of difficulties in nozzle manufacturing. A novel type of cavitation central-body nozzle in which the central-body is perpendicular to the jet is proposed in this study. This new nozzle can produce good cavitation jet and it is much easier for manufacture. The exit of the new nozzle is designed to be square because, compared to the round-outlet central-body nozzle, the square-outlet central-body nozzle can induce more cavitation. The bubbles volume fraction distribution along the axis of the jet produced by square-outlet and round-outlet central-body nozzles is shown in Fig. 1. As it is shown in Fig. 1 that the bubbles spread 7 mm with the jet in square-outlet central-body nozzle while the bubbles from the round-outlet nozzle collapse quickly as soon as reaching the outside. are changed. (3) The effects of outlet length on the cavitation jet are analyzed when the values of d 1, d 2, d 3, d 4 are unchanged and set up two values of L 1. The specific parameters are shown in Table 1. Fig. 1. Volume fraction of bubbles along the axis of the jet produced by square-outlet and round-outlet central-body nozzles In this paper, the jet flow field of square exit central-body nozzle is presented. The effects of nozzle structure parameters, the central-body s relative diameter, the contraction degree and the length of outlet part, on the jet characteristics are focused on to explore major factors affecting cavitation jet. 2 Physical Model Fig. 2 shows the structure of the nozzle. Equivalent inner diameter of nozzle s outlet d 1, central-body s diameter d 2, diameter of the transition contraction d 3, length of outlet part L 1 and diameter of the channel intersecting with the central-body axis line d 4 are marked. Define Bd 2 d 4 as 2 2 the central-body relative diameter and A4d1 πd3 as contraction degree. The following situations are simulated and analyzed. (1) Three cases of contraction degree, A0.6, A0.39, A0.32 and A0.12, are set up when changing d 1 and keeping d 3 1.6 mm, to study the effect of A on the cavitation jet. (2) The forms of the cavitation jet are analyzed with different B when d 4 is set to fixed value and the values of d 2 Fig. 2. Structure of the square-outlet central-body nozzle Table 1. Three structure parameters for the nozzle Parameter 1 2 3 a b c d a b a b Outlet equivalent 0.500 0.800 0.886 1.100 1.660 1.660 0.886 0.886 diameter d 1mm Central-body diameter d 2mm 1.2 2.2 1.2 1.2 1.2 Transition contraction 1.6 3.0 3.0 1.6 1.6 diameter d 3mm Channel intersecting with the central-body axis diameter d 4 mm 1.81 3.34 3.34 1.81 1.81 Outlet length L 1mm 1.0 1.0 1.0 0.5 2.0 Central-body relative diameter 0.66 0.66 0.36 0.66 0.66 B Contraction degree A 0.12 0.32 0.39 0.60 0.39 0.39 0.39 0.39
478 YANG Minguan, et al: Effect of Geometrical Parameters on Submerged Cavitation Jet Discharged 3 Numerical Simulation 3.1 Governing equations The cavitation jet is modeled by commercial code Fluent 6.3. RNG k-ε turbulence model and full cavitation model are employed for this simulation. The mixture model is adopted for the multiphase flow. The equations are described as follows. Continuity equation is ρm ( ρmvm) 0, (1) t where ρ m Mixture density, v m Mass-averaged velocity. Momentum equation is ( ρmvm) ( ρmvmvm) t T p µ m( vm vm), (2) at no-slip condition and the wall function method is used near the wall. Fig. 3. Calculated flow field 4 Results and Analysis 4.1 Formation of cavitation jet in the novel central-body nozzle It is shown in Fig. 4 that the velocity and turbulent kinetic energy distribution around the central-body and inside the outlet part as the nozzle with such structure parameters, d 1 0.886 mm, A0.39, B0.66. where µ m is the mixture viscosity. Bubble volume fraction equation is ( ρmfv) ( ρmv mfv) ( γfv) ReRc, (3) t where f v Vapor mass fraction, γ Effective exchange coefficient. R e and R c are the vapor generation and condensation rate terms. The rate expressions are derived from the Rayleigh-Plesset equations and are given by V 2( p ) R C ρρ p (1 f ), p p, (4) ch sat e e l v v sat σ 3ρl V 2( p ) R C ρρ p f, p p, (5) ch sat c c l v v sat σ 3ρl where V ch Characteristic velocity, σ Surface tension coefficient of the liquid, p sat Liquid saturation vapor pressure, p sat 2 367 Pa at 20, C e, C c Empirical constants, C e 0.02, C c 0.01. The governing equations are dispersed with the finite volume method. The SIMPLEC method is adopted for pressure-velocity coupling. 3.2 Boundary conditions As is shown in Fig. 3 that an area of 50 mm21 mm21 mm is created outside the nozzle exit in the calculated flow field. The inlet pressure of the nozzle is set to be 15 MPa and the outlet pressure is 0.1 MPa. The injection is pure water at room temperature and the ambient media outside the nozzle exit is also pure water. All solid boundaries are Fig. 4. Velocity and the turbulent kinetic energy distributions around the central-body and inside the outlet part It can be seen in Fig. 4(a) that when the fluid runs across the cylindrical central-body, the flow velocity increases in the right and left sides of the central-body and the back-sides close to the contractive section. Low pressure is prone to be formed in the above two regions because of the separation of the boundary layer. The flow rate further increases in the outlet section and an area of low pressure comes up in the initial wall of the outlet part. In Fig. 4(b) it can be found that the area of high turbulent kinetic energy is in the behind of central-body and the initial boundary of the outlet part, where is existing large scale vortexes. The primary bubbles which come into being in this area as the
CHINESE JOURNAL OF MECHANICAL ENGINEERING 479 pressure under the local vapor pressure will develop when spreading outside with the jet. 4.2 Effect of contraction degree on the cavitation jet Cases of four nozzles with different contraction degree in the first group (Table 1) are calculated. The pressure distribution is showed in Fig. 5. Fig. 5(a) Fig. 5(d) show the pressure distribution around the central-body in x0 mm cross-section. Fig. 5(e) is the pressure distribution in radial direction in the 0.1 mm cross-section of outlet part and its partial enlargement. rr 0 is the dimensionless radial distance. The distribution of the bubbles volume fraction is showed in Fig. 6. Fig. 6(a) Fig. 6(d) show the bubbles volume fraction distribution around the central-body of x0 mm section. Fig. 6(e) is the distribution along the axis of the outside jet. dd 0 is the ratio of the axial distance outside the nozzle and the equivalent inner diameter of nozzle s outlet. around the central-body is different with the contraction degree changed. The lowest pressure is in the back of the central-body and the range gets wider in Fig. 5(a) Fig. 5(c) while the lowest pressure is in the back-side of the central-body in Fig. 5(e). The main reasons are as follows: The boundry layer separates earlier as the rate of flow around the central-body increases in the larger contraction degree nozzle. Fig. 5(e) shows that the low pressure which exists in the wall of the outlet initial part is below the local vapor pressure in the four nozzles, so the primary bubbles forms in this area. Moreover, the area with the pressure under the cavitation pressure is larger in radical direction with the contraction degree increased. The scope is close to 0 mm as A0.12 while the cavation region is in the area rr 0 between 0.8 and 1.0 as A0.32, 0.39, and 0.6. Due to the different size of r 0, the larger the contraction degree of the nozzle is, the greater the radical direction scope in the outlet part is. Fig. 5. Pressure distributions in cavitation jet produced by nozzles with different contraction degree (MPa) It can be seen in Fig. 5(a) Fig. 5(d) that the range of low-pressure area which comes into being as the fluid passing around the cylinder central-body is increasing from the back of the central-body to 3/4 area around the central-body when the contraction degree is getting larger from 0.12 to 0.6. The position of the lowest pressure Fig. 6. Volume fraction of bubbles distribution in nozzles with different contraction degrees Fig. 6(a) Fig. 6(d) show that the incipient bubbles which forms in initial inner wall of the outlet part and the low-pressure area around the central-body will spread to the jet center and then spread outside with the jet. The
480 YANG Minguan, et al: Effect of Geometrical Parameters on Submerged Cavitation Jet Discharged incipient cavitation cloud in the initial inner wall of the outlet section increases and extends to the outlet end face along the wall with the contraction degree increasing. It can be found in Fig. 6(e) that the bubbles of which the volume fraction is highest, nearly 70% and 80%, in 5 6 mm outside the nozzle spread outside 8 9 mm with the jet in the nozzles as A0.32 and A0.39. The bubbles collapse as soon as extending to the outside as A0.12 and A0.6. The main reason is that the bubbles produced in the initial inner wall of the outlet section are rare as A0.12 while the bubbles of which the scope extends to the end face of the outlet as A0.6 collapse quickly in the jet edge with a high pressure. Based on an overall consideration of Fig. 5 and Fig. 6, it can be found that the distribution of low-pressure area around the central-body and in the outlet section, and the incipient bubbles are both increasing with the contraction degree increased, however the profile of cavitation jet is following the same change regularity.when B0.66 and d 3 1.6 mm, a good cavitation jet forms in the nozzle with a right contraction degree, because a large amount of incipient bubbles that come into being in the inner wall diffuse to the core of the jet in the outlet section and spread a far distance outside the nozzle with the jet at that case. 4.3 Effect of central-body relative diameter on the cavitation jet Two nozzles with different central-body relative diameters are calculated. The pressure distribution and the volume fraction of bubbles in x0 mm section is showed in Fig. 7. The velocity distribution around the central-body and the axial velocity distribution along the jet axis are respectivly displayed in Fig. 8 and Fig. 9. dd 0 is the ratio of the axial distance outside the nozzle and the equivalent inner diameter of nozzle s outlet. Fig. 7. Pressure and volume fraction of bubbles distribution in x0 mm section of nozzles with different central-body relative diameter Fig. 8. Velocity distribution around the central-body of nozzles with different relative central-body diameter (ms) Fig. 9. Axial velocity distribution on the jet axis outside the nozzles with different relative central-body diameter Fig. 7 shows that the pressure distributions around the central-body are in some differences when the central-body relative diameters are not the same. The low pressure distributes in the periphery and back area of the central-body about 23 rang around the central-body as B= 0.66 while the low pressure is mainly in the back of the central-body just 12 rang as B=0.36. The main reason for the different pressure distribution is as follows: The flow rate is up to 100 ms (Fig. 8) in the narrow channel between the central-body and the solid wall and the pressure is relatively low in that area as B=0.66, while the flow rate is 60 ms (Fig. 8) in the relatively wider channel and the pressure is relatively higher in the nozzle with smaller central-body relative diameter. It can be seen in Fig. 7 that the volume fraction distributions of bubbles are significantly different in cases of with different central-body relative diameters: Most of the bubbles are in the core of the jet beam, less in the boundary of the jet beam as B0.66. On the contrary, most of the bubbles are in the boundary of the jet beam as B=0.36. The bubbles distribution also has an obvious relationship with the velocity distribution. In Fig. 9, the initial segment of jets in two nozzles are both long up to 10 mm. But the flow rate outside the nozzle is close to 170 ms in the nozzle as B0.36 because of its less energy loss while the flow rate is 150 ms as B0.66. The incipient bubbles can spread to the core of the jet because of the relatively lower flow rate as spreading with the jet, forming a cavitation jet with bubbles mainly in the core of jet beam. In the nozzle with smaller central-body diameter the bubbles which spread to outside directly with high-speed jet mainly distribute in the boundary of jet beam. At the same time the jets with higher
CHINESE JOURNAL OF MECHANICAL ENGINEERING 481 velocity and longer initial section in the two nozzles have a strong shear with the static liquid in the jet boundry, forming the shear cavitation, which increases the bubbles in the edge of the jet beam. 4.4 Effect of outlet part length on the cavitation jet Two nozzles with different outlet length are compared. The pressure distribution and the volume fraction of bubbles in x0 mm cross-section are shown in Fig. 10. It can be seen from Fig. 10 that the pressure distribution around the central-body is almost same in the two nozzles but the volume fraction distributions of bubbles are in great differences. It is in the outlet segment where the scope and volume fraction of the bubbles are the largest as L 1 2.0 mm and the outside diffusion distance of the bubbles is only 3 mm. As L 1 0.5 mm, the scope and the volume fraction of the bubbles is the largest one in a distance of 3 mm outside the outlet, and the diffusion distance of bubbles is twice long up to 6 mm. The results is the same with the Beutin s research [11] in the plunger central-body nozzle. In his study it was found that the optimum spray distance increased with the length of the nozzle pipe shorten. Therefore the shorter outlet nozzle will have a longer target distance and greater target range if applied to broke rock. Length is not as short as possible because the nozzle with too short outlet has negative effect on the forming region of the incipient bubbles, which reduces the amount of the bubbles. quickly outside the outlet for the first three nozzles while the bubbles have a great development in the latter two cases. In Fig. 11(f) it can be seen that the flow rate outside the outlet decays rapidly in the first three cases while in the latter two cases the initial segment of jets are long to 10 mm. Therefore, when the scope of the incipient bubbles extends to the outside, there is a great relevance between the attenuation trend of the jet velocity and development of the bubbles: The pressure rises when the flow rate decays rapidly, which causes quick collapse of the bubbles; The bubbles can spread a long distance with the jet as the jet velocity with a long initial segment, furthermore the jet with high velocity and a long initial segment can also cause the incipient bubbles in the jet boundary. Fig. 10. Pressure and volume fraction of bubbles distribution in x0 mm section of nozzles with different outlet length 4.5 Effect of exit jet velocity on the cavitation jet Fig. 11 shows the volume fraction of bubbles and outside jet velocity of five nozzles with different structure parameters. It can be seen that the incipient bubbles extend to the outside of the outlet section in all of the five different nozzles, but the extension of the bubbles outside the nozzles are in significant differences. The bubbles collapse Fig. 11. Distribution of volume fraction of bubbles in x0 mm section and the velocity along the axial direction of five nozzles with different structure parameters
482 YANG Minguan, et al: Effect of Geometrical Parameters on Submerged Cavitation Jet Discharged 5 Conclusions (1) When the contraction degree and the central-body diameter of the nozzle has the best match in the nozzle, a right low pressure area will be generated around the central-body and in the initial inner wall of the outlet section where a large amount of incipient bubbles come into being and does not extend to the outside along the inner wall, which leads to a better cavitation jet. (2) The size of central-body equivalent diameter will affect the distribution of bubbles in the jet beam: The bubbles mainly distribute in the center of jet beam in the nozzle with large central-body equivalent diameter, and when central-body equivalent diameter is small the bubbles mainly distribute in the boundary of jet beam. (3) The jets are in some differences in nozzles with different outlet section length: the distribution of bubbles outside the nozzle with long outlet section is short and narrow while the scope of bubbles is long and wide outside the nozzle with short outlet section. (4) The distribution of bubbles in the jet flow field has a great connection with the number of initial bubbles, but also has much to do with the outside jet velocity: When the incipient bubbles extended outside, they have a great development outside the nozzle which forms a jet with long initial segment and the bubbles collapse quickly outside the nozzle as the initial segment of the jet short. The experiments will be carried on in the next step, using PIV, high-speed digital video camera and other methods to verify the correlations between of the above conclusions. And against damage experiment will be done to analyze the effect of structure parameters of the central-body nozzle on cavitation jet. 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Beijing: Geology Press, 1986. [16] LIU Yanling. Modulation study on unsubmerged cavitating jetfrom nozzle with a centre cylinder[d]. Qingdao: China University of Petroleum, 2009. (in Chinese) [17] YANG Minguan, ZHANG Feng, KANG Can, etal. Experiment and numerical simulation of free water jet by a central-body nozzle[j]. Chinese Journal of Mechanical Engineering, 2010, 23(6): 797 804. Biographical notes YANG Minguan, born in 1952, is currently a professor and a PhD candidate supervisor at School of Energy and Power Engineering, Jiangsu University, China. His main research interests include fluid mechanical properties and internal multiphase flow. Tel: +86-511-83355570; E-mail: mgyang@ujs.edu.cn XIAO Shengnan, born in 1986, is currently a master candidate at School of Energy and Power Engineering, Jiangsu University, China. Her main research interests include fluid mechanical properties and internal multiphase flow. Tel: +86-15850034020; E-mail: xsn1986@126.com KANG Can, born in 1978, is currently an associate professor at School of Energy and Power Engineering, Jiangsu University, China. His main research interests include fluid mechanical properties and internal multiphase flow. E-mail: kangcan@ujs.edu.cn WANG Yuli, born in 1984, is currently a PhD candidate at School of Energy and Power Engineering, Jiangsu University, China. His main research interests include fluid mechanical properties and internal multiphase flow. E-mail: zcjwyl@163.com