CIESC Journal ›› 2019, Vol. 70 ›› Issue (2): 487-495.doi: 10.11949/j.issn.0438-1157.20181220

• Process system engineering • Previous Articles     Next Articles

Generality of CFD-PBM coupled model for simulations of gas-liquid bubble column

Huahai ZHANG(),Tiefeng WANG()   

  1. Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
  • Received:2018-10-17 Revised:2018-12-16 Online:2019-02-05 Published:2019-04-03
  • Contact: Tiefeng WANG E-mail:950826zhh@sina.com;wangtf@tsinghua.edu.cn

Abstract:

The generality of the CFD-PBM coupled model was studied by comparing the simulation results with experimental data under different operating pressures and liquid properties. The results show that the CFD-PBM coupled model with the modified pressure factor obtained from the internal-flow bubble breakup model can well predict the influence trend of pressure on the hydrodynamics of bubble column. The gas holdup increases significantly with increasing pressure. In addition, the simulation results for different liquid viscosity and surface tension are consistent with the experimental results. With increasing liquid viscosity, the bubble breakup rate decreases, which leads to a wider bubble size distribution, lower drag correction factor and decreased gas holdup. As the surface tension decreases, the bubble breakup rate increases, which results in smaller bubbles and higher gas holdup. The CFD-PBM coupling model has good versatility because it considers the effects of pressure, liquid viscosity and surface tension on bubble coalescence, fracture and gas-liquid interaction.

Key words: bubble column, CFD-PBM coupled model, operating pressure, physical properties, gas holdup

CLC Number: 

  • TQ 021.1

Fig.1

Schematic diagram of CFD-PBM model"

Table 1

Governing equations of two-fluid model"

模型主要方程和关联式
质量守恒方程??(ραu)i=0, i = g, l
动量守恒方程??(ραuu)i=-αi?P'+??αμeff(?u+?uT)i+Fi,j+(ρα)ig, i = g, l
液相k-ε模型
k方程??(ρlαlklul)i=??αlμlam,l+(μt,l+μtb)/σk?kl+αl(Gk,l-ρlεl)
ε方程??(ρlαlεlul)i=??αlμlam,l+(μt,l+μtb)/σε?εl+αlεlkl(Cs1Gk,l-Cs2ρlεl)

湍动能产生项

液相湍动黏度

Gk,l=μeff,l?ul??ul+?ulT-23??ulμeff,l??ul+ρlkl

μt,l=Cμ(ρlkl2/εl)

湍能修正

μeff,l=μlam,l+μt,l+μtb,μtb=Cμbρlαgdbsug-ul

kl,t=kl+kl,g,εl,t=εl+εl,g,kl,g=12αgCVMuslip2,εl,g=αgguslip

气相湍动黏度μt,g=μt,lρg/ρl
相间作用力

曳力

FD=CDCD0i=1Mfiαgρl3CDi4dbi(ug-ul)ug-ul

CDi=max24Rei-11+0.15Rei0.687,83Eo/(Eo+4)

CD/CD0=kb,largekb,small,kb,large=1/max(1.0,90.0αgfb,large),kb,small=1-αg,small1+22αg,small/Eo+0.4

虚拟质量力FVM=αgρlCVMDDt(ug-ul),CVM=0.25

横向升力

FL=-i=1MfiCLiαgρl(ug-ul)?ul?r

CLi=min(0.288tanh(0121Rei),f(Eoi'))Eoi'<3.4f(Eoi')3.4<Eoi'<5.3-0.29Eoi'>5.3

f(Eoi')=0.00925Eoi'3-0.0995Eoi'2+1.088

湍动扩散力FTD=-CTDαgρlkl?α?r
壁面润滑力FW=-i=1M12fiCWiαgdbiR-r-2-R+r-2ρlug-ul2

Table 2

Models of bubble breakup and coalescence"

模型主要方程和关联式
由湍流涡引起的破碎
破碎速率b(d)=00.5b(fvd)dfv
子气泡大小分布β(fv,d)=2b(fvd)01b(fvd)dfv-1

补充方程

bfvd=Bbfv'd,B=ρg70d-2800d2d<0.018ρg0.35d0.018

bfv'd=0.9231-αdnε1/3λmindbPbfv'd,λλ+d2λ-11/3dλ

Pbfvd,λ=0Pbfvd,e(λ),λPe(e(λ))de(λ)

Pe(e(λ))=(1/eˉ(λ))exp(-e(λ)/eˉ(λ)),eˉ(λ)=112πλ3ρcuˉλ2

cf,max=min(21/3-1),e(λ)/(πd2σ),fv,min=πλ3σ/(6e(λ)d3

Pbfv'd,eλ=fv,max-fv,min-1fv,max-fv,minδ&fv,min<fv'<fv,max0else

由大气泡不稳定引起的破碎
破碎速率b2(d)=b(d-dc2)m/(d-dc2)m+dc2m
子气泡大小分布β(fv,d)=2δ(0.5)
湍流涡引起的聚并速率:ct=?tPt

碰撞频率

?tdi,dj=14παg,maxαg,max-αg-1Γij2ε1/3di+dj2di2/3+dj2/31/2

Γij=lbt,ijm/(lbt,ijm+hbt,ijm),lbt,ij=lbt,i2+lbt,j2,lbt=0.89db,hb,ij=(Ni+Nj)1/3

聚并效率Pt(di,dj)=exp-0.75(1+ξij2)(1+ξij3)1/2(ρg/ρl+γ)-1(1+ξij)-3Weij1/2
不同上升速度引起的聚并:cu=?uPu
碰撞频率?udi,dj=14παg,maxαg,max-αg-12ε1/3di+dj2di2/3+dj2/31/2
聚并效率Pu(di,dj)=0.5
大气泡尾涡引起的聚并:cw=?wPw

碰撞频率

?w(di,dj)=12.0Θdi2uˉslip,i,?w(di,dj)=15.4di2uˉslip,i,uˉslip,i=0.71gdi

Θ=(dj-dc/2)6/(dj-dc/2)6+(dc/2)6fordjdc/2;

Θ=0fordj<dc/2withdc=4σ/(gΔρ)

聚并效率Pw(di,dj)=exp-0.46ρl1/2ε1/3σ-1/2didj/(di+dj)5/6

Table 3

Properties of different liquids"

液体密度/(kg/m3)黏度/(Pa·s)表面张力/(mN/m)
[7,11,25,26]10000.00172.5
葡萄糖A[27,28]13400.1776.0
葡萄糖B[27]13800.5576.0
甲苯[29]8660.0005828.5

Fig.2

Comparison of simulated and experimental average gas holdup at different operating pressures[22]"

Fig.3

Mechanism of pressure effect"

Fig.4

Comparison of calculated and experimental average gas holdup at different liquid viscosities"

Fig.5

Calculated bubble size distributions at different liquid viscosities"

Fig.6

Calculated drag correction coefficient at different liquid viscosities"

Fig.7

Mechanism of effect of liquid viscosity"

Fig.8

Comparison of calculated and experimental average gas holdup at different liquid surface tension"

Fig.9

Mechanism of effect of liquid surface tension"

"

vivk——气泡体积,m3
αg——鼓泡床内气含率
β(v,v′)——子气泡分布
δj,k——狄拉克函数
ε——湍流耗散速率,m2/s3
ζ1,ζ2——分别为气泡颈部流动收缩和扩张系数
λ——湍流涡尺寸,m
λmin——破碎最小湍流涡尺寸,m
μ——液体黏度,Pa·s
ρgρl——分别为气体和液体密度,kg/m3
σ——液体表面张力,mN/m
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