J. Cent. South Univ. Technol. (2008) 15(s1): 140-144
DOI: 10.1007/s11771-008-333-z
Numerical simulation of gas-liquid two-phase jet flow in air-bubble generator
CHEN Wen-yi(陈文义)1, WANG Jing-bo(王静波)2, JIANG Nan(姜 楠)3, ZHAO Bin(赵 斌)1,
WANG Zhen-dong(王振东)3
(1. Department of Process Equipments and Control Engineering, Hebei University of Technology,
Tianjin 300130, China;
2. Department of Mineral Processing Engineering, Heilongjing Institute of Science and Technology,
Harbin 150027, China;
3. Department of Mechanics, Tianjin University, Tianjin 300072, China)
Abstract: Air-bubble generator is the key part of the self-inspiration type swirl flotation machines, whose flow field structure has a great effect on flotation. The multiphase volume of fluid (VOF), standard k-ε turbulent model and the SIMPLE method were chosen to simulate the present model; the first order upwind difference scheme was utilized to perform a discrete solution for momentum equation. The distributing law of the velocity, pressure, turbulent kinetic energy of every section along the flow direction of air-bubble generator was analyzed. The results indicate that the bubbles are heavily broken up in the middle cross section of throat sect and the entrance of diffuser sect along the flow direction, and the turbulent kinetic energy of diffuser sect is larger than the entrance of throat sect and mixing chamber.
Key words: air-bubble generator; numerical simulation; flow field; breaking
1 Introduction
Bubble is an indispensable factor in foam flotation; an effective bubble generation device should produce fine and uniform bubbles under the maximum air flow, so study on the bubble producer is one of significant aspects of research on self-inspiration type swirl flotation machines. The work principle of air-bubble generator is that airflow is sucked by high speed jet flows, shorn, torn and mixed to a lot of bubbles with small diameter and more mixing and reaction in the hollow throat, mass and energy transfer are performed by turbulent diffusivity. Air-bubble generator has multiple action with inspiring air, breaking air into bubbles and bubble mineralization, its performance directly determines volume fraction, bubble size and distribution, and has a direct influence on separation effect of flotation machine, so the study on air-bubble generator structure and related parameters calculation are very important, but structure design and calculation is difficult due to the multiphase flow complexity in interior of air-bubble generator[1-5].
2 Numerical simulation method
2.1 Control equation
Continuity equation:
(1)
Momentum equation:
(2)
k equation:
(3)
ε equation:
(4)
where t is time; ui and xi are velocity component and coordinates component, respectively; ρ and μ are density and viscosity coefficient of molecular, respectively; p is modified pressure; μt is turbulent viscosity, it is defined by turbulent kinetic energy and turbulent dissipation rate:
(5)
where Cμ is empirical constant, Cμ=0.09; σk and σε are Prandtl number of 
and ε, σk=1.0, σε=1.3; C1ε and C2ε are constants of ε equation, C1ε=1.44, C2ε=1.92. G is defined as
(6)
it represents the generation term of turbulent kinetic energy caused by mean velocity gradient.
2.2 Boundary conditions and simulation methods
The geometrical model of computation domain with boundary conditions is shown in Fig.1. Inlet diameter of two phases is 40 mm, nozzle diameter is 18 mm, nozzle outlet velocity is 15 m/s, wall thickness is 10 mm, and outlet diameter is 91.7 mm.
Fig.1 Physical model of air-bubble generator
The control equations are discreted with the finite volume method and velocity-pressure is solved coupling with SMIPLE (semi-implicit method for pressure-linked equations), no-slip condition for gas-liquid boundary and temperature was constant. The multiphase volume of fluid (VOF) and k-ε[7-8] turbulent model were chosen to simulate the present flows, the first order upwind difference method was utilized to perform a discrete solution for momentum equation where water was treated as the primary phase. The CFD started when inlet1 to nozzle was full of the primary phase, the rest was the second phase.
3 Results and discussion
3.1 Distribution of radial velocity in different Sections
The distribution of the velocity of different sections is shown in Fig.2. Fig.2(a) shows the distribution of velocity of the center cross section of gas inlet across mixing chamber, it can be seen that comparing with liquid velocity in nozzle, gas velocity is larger, there is gas vortex in mixing chamber, and the external surface of nozzle is encompassed by gas along flow entrance which extends all around the nozzle ektexine; Fig.2(b) shows the velocity distribution at the throat inlet. It appeared that the velocity along the centerline of jet flow core area is the highest and it decreases with the radius increasing, the jetting liquid entrains gas into throat under the function of viscosity between gas and boundary layer of jet flow, and produces velocity fluctuation and surface waves influenced by external disturbance. The distribution of velocity of the cross section inside throat is shown in Fig.2(c), the velocity distribution is the same as that of throat inlet, however, the region of high speed enlarges and velocity value of high speed zone is less than that of throat inlet. Fig.2(d) shows the velocity distribution inside the diffuser. It can be noticed that the region of high velocity jet decreases obviously, and the velocity decreases with the radius increasing; there exists vortex nearby surface and velocity fluctuation is obviously from center to wall.
The velocity distribution of different cross sections along flow direction indicates that there exists intense gas pulsed in the mixing chamber after gas is inhaled from mixing chamber entrance; the high speed motion liquid entrains low velocity gas and enters into throat together, the liquid is located in central area and encompassed by intense pulsating flow near the edge, and velocity distribution is fuzzy gradually at dividing line between liquid and gas. The above results indicate that there occur the intense kinetic energy exchange between these two phases and the variation of velocity gradient forms shear stress which can make two phases break, shear and disperse into microbubbles. The exchange of kinetic energy is distributed to the whole cross section of diffuser, the turbulent eddies and gas-liquid two-phase outflow after thorough mixing are formed by the influence of outlet boundary conditions and energy consumption caused by kinetic energy conversion to pressure energy.
3.2 Distribution of radial pressure in different sections
Fig.3 shows the pressure of different sections. Fig.3(a) shows the distribution of pressure of the center cross section of gas inlet across mixing chamber, the pressure at the nozzle is very high, but the pressure of mixing chamber is relative low. Fig.3(b) shows the distribution of pressure at the throat inlet, it appeared that the pressure is negative number and less than mixing chamber obviously, the negative pressure value decreases
gradually from central part outwards until the wall of throat. The distribution of pressure of the cross section of inside throat is shown in Fig.3(c). The pressure is a little higher than that of throat inlet, but is still in vacuum region. The distribution of pressure of diffuser is shown in Fig.3(d). It can be seen that gas-liquid two-phase runs out of diffuser in the form of foam flow because mixture can transform the kinetic energy into pressure energy after entering into diffuser.
Fig.2 Comparison of velocity in different sections: (a) Center cross section of gas inlet across mixing chamber; (b) Cross section of throat entrance; (c) Cross section of throat; (d) Cross section of diffuser
Fig.3 Comparison of pressure in different sections: (a) Center cross section of gas inlet across mixing chamber; (b) Cross section of throat entrance; (c) Cross section of throat; (d) Cross section of diffuser
The pressure distribution shows that the pressure is negative from mixing chamber to throat outlet, the negative pressure inside throat decreases gradually along the flow direction and pressure pulsation seriously; the pressure becomes positive and distributes uniformly in diffuser, which indicates that gas-liquid two-phase is in good mixing state.
3.3 Distribution of radial turbulent kinetic energy in different sections
Fig.4 shows the turbulent kinetic energy of different sections. It can be noticed that the distribution of turbulent kinetic energy of the center cross section of gas inlet across mixing chamber from Fig.4(a), there are two big turbulence eddies in the inferior partial of mixing chamber between the external wall of nozzle and inner wall of mixing chamber; Fig.4(b) shows the turbulent kinetic energy distribution at the throat inlet, the turbulent kinetic energy is comparatively small in central area, and increases gradually from the center to the edge of throat; the turbulent kinetic energy distribution of the cross section inside throat is shown in Fig.3(c). The turbulent kinetic energy is less than that of throat inlet, comparatively small in central area, and with increasing gradually from the center to the edge of throat, the turbulent kinetic energy fluctuates violently; Fig.4(d) shows the turbulent kinetic energy distribution inside the diffuser. It appears that the turbulent kinetic energy is obviously higher than those of mixing chamber and throat, the intense pulsation region of turbulent kinetic energy is the middle area between wall and center.
The turbulent kinetic energy distribution shows that the turbulent kinetic energy distribution inside the diffuser is obviously higher than those of mixing chamber and throat. The turbulent kinetic energy inside throat extends gradually from wall to center, and with the values decreasing the turbulent kinetic energy fluctuates violently, the numerical value variation of turbulent kinetic energy at the cross section of diffuser is obvious. The turbulent kinetic energy pulsation of throat inlet and diffuser indicates that the intense turbulent kinetic energy produces shear stress in the region of throat and diffuser where intensive shearing, breaking, mixing and energy transfer can occur.
Fig.4 Comparison of turbulent kinetic energy of different sections: (a) Center cross section of gas inlet across mixing chamber; (b) Cross section of throat entrance; (c) Cross section of throat; (d) Cross section of diffuser
4 Conclusions
1) It is negative pressure zone at throat inlet and throat, which is helpful to suck air continuously, and complete self-inspiration and form bubbles.
2) Gas phase produces shear stress under the effect of turbulent in the throat, which can make gas-liquid two-phase break, disperse and mix between them. As pressure increases, bubbles are compressed, split into microbubbles.
3) The turbulent kinetic energy of diffuser is larger than that of throat and mixing chamber.
5 Acknowledgements
Support for this research was provided by Professor CHEN Yao-song from the Department of Mechanics of Beijing University.
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(Edited by HE Xue-feng)
Foundation item: Project supported by the Scientific Research Foundation of Hebei University of Technology of China
Received date: 2008-06-25; Accepted date: 2008-08-05
Corresponding author: CHEN Wen-yi, Professor, PhD; Tel: +86-22-60204794; E-mail: cwy63@126.com
