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Frontiers of Chemical Science and Engineering

ISSN 2095-0179

ISSN 2095-0187(Online)

CN 11-5981/TQ

Postal Subscription Code 80-969

2018 Impact Factor: 2.809

Front Chem Sci Eng    2011, Vol. 5 Issue (2) : 162-172    https://doi.org/10.1007/s11705-009-0267-5
REVIEW ARTICLE
Simulation of bubble column reactors using CFD coupled with a population balance model
Tiefeng WANG()
Beijing Key Laboratory of Green Reaction Engineering and Technology, Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
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Abstract

Bubble columns are widely used in chemical and biochemical processes due to their excellent mass and heat transfer characteristics and simple construction. However, their fundamental hydrodynamic behaviors, which are essential for reactor scale-up and design, are still not fully understood. To develop design tools for engineering purposes, much research has been carried out in the area of computational fluid dynamics (CFD) modeling and simulation of gas-liquid flows. Due to the importance of the bubble behavior, the bubble size distribution must be considered in the CFD models. The population balance model (PBM) is an effective approach to predict the bubble size distribution, and great efforts have been made in recent years to couple the PBM into CFD simulations. This article gives a selective review of the modeling and simulation of bubble column reactors using CFD coupled with PBM. Bubble breakup and coalescence models due to different mechanisms are discussed. It is shown that the CFD-PBM coupled model with proper bubble breakup and coalescence models and interphase force formulations has the ability of predicting the complex hydrodynamics in different flow regimes and, thus, provides a unified description of both the homogeneous and heterogeneous regimes. Further study is needed to improve the models of bubble coalescence and breakup, turbulence modification in high gas holdup, and interphase forces of bubble swarms.

Keywords bubble column      computational fluid dynamics      bubble breakup and coalescence      population balance model      bubble size distribution     
Corresponding Author(s): WANG Tiefeng,Email:wangtf@tsinghua.edu.cn   
Issue Date: 05 June 2011
 Cite this article:   
Tiefeng WANG. Simulation of bubble column reactors using CFD coupled with a population balance model[J]. Front Chem Sci Eng, 2011, 5(2): 162-172.
 URL:  
https://academic.hep.com.cn/fcse/EN/10.1007/s11705-009-0267-5
https://academic.hep.com.cn/fcse/EN/Y2011/V5/I2/162
Fig.1  Bubble breakup and coalescence due to different mechanism
authordaughter size distributionIIIIIIIVVVItypical result
Alentas et al. (1966) Prince et al. (1990)β(fv,d)=δ(fv,0.5)XX?X?XValentas et al. (1966)Lee et al., (1987)
Lee et al. (1987)β(v1,v)=Γ(a+b)Γ(a)Γ(b)v1(v1v)a-1(1-v1v)b-1?X??
Hesketh et al. (1991)β(d1,d)=(1(d1/d)3+B+11-(d1/d)3+B-2(B+0.5))Id3X?X?Hesketh et al. (1991)Nambar et al.(1992)
Nambiar et al. (1992)β(v1,v)=4sin?|π-2?3|f(λ|λmin?λd)πλdsin??????XX
Tsouris et al. (1994)β(d1,d)=emin?+(emax?-e(d1))d1min?d0emin?+(emax?-e(d1))dd1XXX?X?Tsouris et al. (1994)Luo et al.(1996)
Luo et al. (1996)β(fv,d)=2ξmin?1(1+ξ)2ξ-11/3exp?(-χc)dξv01ξmin?1(1+ξ)2ξ-11/3exp?(-χc)dξdfv??X???
Martínez-Bazán et al. (1999)β(d1,d)d=(d?2/3-Λ5/3)((1-d?3)2/9-Λ5/3)dmin??dmax??(d?2/3-Λ5/3)((1-d?3)2/9-Λ5/3)dd????X??Martínez et al. (1999)Lehr et al.(2001)
Lehr et al. (2001)r1(v1,v)=1.5(1-αd)ρc11/5?9/5σ11/5v^1/3v^14/3(min?(v^17/6,1v^17/9)-1v^7/9)#?????X
Tab.1  Daughter size distribution models in the literature
Fig.2  Influence of the mother bubble size and energy dissipation rate on the breakup rate for an air-water system ( = 0.0725 N/m, = 0.01, /λ = 31.4)
itemsequations
bubble breakup due to turbulent eddiesbreakup rateb(d)=00.5b(fv|d)dfv
daughter bubble size distributionβ(fv,d)=2b(fv|d)(01b(fv|d)dfv)-1
complement equationsb(fv|d)=0.923(1-αd)n?1/3λmindbPb(fv|d,λ)(λ+d)2λ-11/3dλ, Pb(fv|d,λ)=0Pb(fv|d,e(λ),λ)Pe(e(λ))de(λ)Pe(e(λ))=(1/eˉ(λ))exp?(-e(λ)/eˉ(λ)), eˉ(λ)=112πλ3ρcuˉλ2cf,max?=min?((21/3-1),e(λ)/(πd2σ)),fv,min?=(πλ3σ/(6e(λ)d))3, Pb(fv|d,e(λ),λ)={(fv,max?-fv,min?)-1fv,max?-fv,min?δ&fv,min?<fv<fv,max?0else
bubble breakup due to instability of large bubblesbreakup rateb2(d)=b?(d-dc2)m/((d-dc2)m+dc2m)
daughter bubble size distributionβ(fv,d)=2δ(0.5)
coalescence rate due to turbulent eddies: ct = vtPtcollision rate?t(di,dj)=14παg,max?(αg,max?-αg)-1Γij2?1/3(di+dj)2(di2/3+dj2/3)1/2Γij=lbt,ijm/(lbt,ijm+hb,ijm), lbt,ij=lbt,i2+lbt,j2, lbt=0.89db, hb,ij=(Ni+Nj)1/3
coalescence efficiencyPt(di,dj)=exp?(-(0.75(1+ξij2)(1+ξij3))1/2(ρg/ρl+γ)-1(1+ξij)-3Weij1/2)
coalescence rate due to different rise velocity: cu = vuPucollision rate?u(di,dj)=14παg,max?(αg,max?-αg)-12?1/3(di+dj)2(di2/3+dj2/3)1/2
coalescence efficiencyPu(di,dj)=0.5
coalescence due to bubble wake: cw = vwPwcollision rate?w(di,dj)=KΘdi2uˉslip,i?w(di,dj)=15.4di2uˉslip,i, uˉslip,i=0.71gdiΘ=(dj-dc/2)6/((dj-dc/2)6+(dc/2)6)for djdc/2;Θ=0 for dj<dc/2. with dc=4σ/(gΔρ)
coalescence efficiencyPw(di,dj)=exp?(-Kwρl1/2?1/3σ-1/2(didj/(di+dj))5/6)
Tab.2  Models of bubble breakup and coalescence
Fig.3  Influence of the mother bubble size on daughter bubble size distribution for an air-water system []
( = 0.0725 N/m, = 0.01, / = 31.4)
Fig.4  Simulation of gas-liquid mass transfer with the framework of the CFD-PBM coupled model []
modelsequations
mass conservation?·(ραu)i=0, i = g, l
momentum conservation?·(ραuu)i=-αi?P+?·(αμeff(?u+?uT))i+Fi,j+(ρα)ig, i = g, l
k-? turbulence model for the liquid phasek equation?·(ρlαlklul)=?·(αl(μlam,l+(μt,l+μtb)/σk)?kl)+αl(Gk,l-ρl?l)
? equation?·(ρlαl?lul)=?·(αl(μlam,l+(μt,l+μtb)/σ?)??l)+αl?lkl(C?1Gk,l-C?2ρl?l)
generation rate and eddy viscosityGk,l=μeff,l?ul·(?ul+(?ul)T)-23?·ul(μeff,l?·ul+ρlkl), μt.l=Cμ(ρlkl2/?l)
turbulence modificationμeff,l=μlam,l+μt,l+μtb, μtb=Cμbρlαgdbs|ug-ul|kl,t=kl+kl,g, ?l,t=?l+?l,g, kl,g=12αgCvmuslip2, ?l,g=αgguslip
turbulent viscosity of the gas phaseμt,g=μt,lρg/ρl
interphase forcesdrag forceFD=i=1Mfiαgρl3CDi4dbi(ug-ul)|ug-ul|, CDi=max?[24Rei-1(1+0.15Re?i0.687),83Eo/(Eo+4)]
virtue mass forceFV=αgρlCVDDt(ug-ul)
transverse lift forceFL=-i=1MfiCLiαgρl(ug-ul)?ul?r, CLi={min?(0.288tanh?(0.121Re?i),f(Eoi))Eoi<3.4f(Eoi)3.4<Eoi<5.3-0.29Eoi>5.3f(Eoi)=0.00925Eoi3-0.0995Eoi2+1.088
turbulent dispersion forceFTD=-CTDαgρlkl?α?r
wall lubrication forceFW=-i=1M12fiCWiαgdbi[(R-r)-2-(R+r)-2]ρl(ug-ul)2
Tab.3  Governing equations of the two-fluid model
Fig.5  Comparison of measured and simulated average gas holdup [,]
(Parameters of the simulated column: i.d. = 0.19 m, = 2.4 m. The results are for height of 2.0 m)
Fig.6  Radial profiles of the gas holdup in a gas-liquid cocurrent upward flow []
Fig.7  Bubble size distributions at different radial positions and superficial gas velocities []
Fig.8  Prediction of the variation of volume fraction of small bubbles with superficial gas velocity []
Fig.9  Comparison of the predicted and measured volumetric mass transfer coefficients []
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