CFD simulation of gas–liquid flow in a hig(2)

Liu et al.[23]introduced a modified drag coefficient CDin the bubble group drag the modified drag model was used in the numerical investigations of the flow characteristics of pressurized churn turbulent bubble column with the operation pressure varying from 0.5 MPa to 2.0 MPa,and superficial gas velocity from 0.20 m·s?1to 0.31 m·s?1.The simulation results can accurately reflect varioushydrodynamic parameters in the bubble refore,their drag coefficient CD[23]is adopted in this work:

dispersion force

In order to simulate the turbulence of the fluid in the high-pressure bubble column,it is necessary to introduce the turbulence diffusion force,which can help in making the gas holdup evenly turbulent diffusion force formula proposed by Lopez de Bertodano[27]is as follows:

CTDisthe coefficient of turbulent diffusion force,and its default value is 1.

If Eq.(8)is used directly in the simulation,the simulation is not easy to ,the limiting function fTD,limitingis introduced into the Fluent 15.0 platform to adjust the turbulent disperation force new expression of the turbulent diffusion force model becomes:

w here εG,1and εG,2was set to be 0.3 and 0.7.

lift force

When the bubble is moving in the liquid,the pressure distribution around the bubble is not balanced due to the asymmetry of the liquid in the direction of the moving air that a transverse lift force is generated perpendicular to the direction of bubble lift force of the discrete phase in the continuous phase given by Drew[20]is.

The coefficients CLand CTDhave different values in the uncertainty reflects the complexity of gasbubble diffusion in turbulent multiphase media and the limitations of prior know [28]considered the parameter CL/CTDas a function of liquid holdup εLand the equation is as follow s:

lubrication force

The bubbles are subjected to a force toward the center,so the bubbles move in the direction away from the wall,and this force is called the wall lubrication velocity dependence on wall lubrication force is clearly shown by Nguyen et al.[29].So the wall lubrication force was introduced in the simulation of gas–liquid flow s.

Tomiyama wall lubrication force model[30]is used in this work:

where CWLis a value from Eq.(14).

and CWis defined as:

The definition of Eo is:

balance model

When the gas contacts with the liquid in the high-pressure bubble column,the dispersed bubbles exist in a broad range of size.A significant attribute of gas–liquid flows is that the bubbles of different sizes interact with each other through the mechanisms of breakup and present,the population balance model(PBM)is used to deal with this general form of the population balance equation is:

breakup model

Because the Luo model has a relatively simple form,high prediction accuracy,it is widely ,the Luo model is adopted in this paper.

in which K,n,m,β,b can be expressed as

coalescence model

The expression of bubble coalescence model[31]is.

The collision frequency between bubbles can be expressed as.

Based on the Luo model and the correction coefficient Ceintroduced,the modified bubble coalescence model is.

In this work,the coalescence resulted from turbulent eddies was eddies cause the bubbles to collide and coalesce with a certain mechanism of pressure on bubble coalescence is not yet clear.Up to now,models for bubble coalescence are mainly based on experimental phenomena by semi-theoretical semiempirical [6]introduced a constant correction coefficient Cein the bubble coalescence ,we find that the correction coefficient Ceis not a constant under different gas velocities and this work,according to the experimental data of Qin[14]from cold experiment,a density correction factor Cecan be obtained by simulation at the apparent gas velocity 0.199,0.233,0.275 m·s?1and the operating pressure at 0.5,1,1.5,2.0 data are shown in Table 1.The linear regression equation between Ceand the gas density is as follow s:

Table 1Coalescence model correction coefficients and the simulated gas holdupsugP/MPa ρ/ρ0CeεexpεsimError of ε 0.199 0.5 5 1.16 0.3573 0.3603 0.83%0.199 1.0 10 1.45 0.4586 0.4593 0.15%0.199 1.5 15 1.50 0.4941 0.5016 1.52%0.199 2.0 20 1.62 0.5321 0.5313 ?0.15%0.233 0.5 5 1.16 0.3937 0.3961 0.61%0.233 1.0 10 1.45 0.4881 0.4910 0.59%0.233 1.5 15 1.50 0.5254 0.5300 0.88%0.233 2.0 20 1.62 0.5523 0.5527 0.07%0.275 0.5 5 1.16 0.4250 0.4333 1.94%0.275 1.0 10 1.45 0.505 0.5200 2.97%0.275 1.5 15 1.50 0.548 0.5500 0.36%0.275 2.0 20 1.62 0.571 0.5774 1.12%

Model and Mesh Generation

The experiment of Qin[14]mainly examined the impact of pressure on the hydrodynamic behaviorsin variousoperating conditionsat 25°C.Air wasused asthe gasphase and water asliquid phase,the gas velocity was varied from 0.119 to 0.312 m·s?1and pressures from 0.5 to 2.0 MPa.

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