Accepted Manuscript Title: CFD Simulation of Pilot-Scale Bubble Columns with Internals: Influence of Interfacial Forces Authors: Xiaoping Guan, Ning Yang PII: DOI: Reference:
S0263-8762(17)30431-8 http://dx.doi.org/10.1016/j.cherd.2017.08.019 CHERD 2794
To appear in: Received date: Revised date: Accepted date:
11-4-2017 7-8-2017 22-8-2017
Please cite this article as: Guan, Xiaoping, Yang, Ning, CFD Simulation of Pilot-Scale Bubble Columns with Internals: Influence of Interfacial Forces.Chemical Engineering Research and Design http://dx.doi.org/10.1016/j.cherd.2017.08.019 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
CFD Simulation of Pilot-Scale Bubble Columns with Internals: Influence of Interfacial Forces Xiaoping Guan1*, Ning Yang1* 1
State Key Laboratory of Multi-phase Complex System, Institute of Process Engineering, Chinese
Academy of Sciences, P.O. Box 353, Beijing 100190, PR China
To
whom correspondence should be addressed. E-mail:
[email protected] (X. Guan),
[email protected] (N. Yang)
Graphical abstract
Highlights
Effects of interfacial forces in bubble columns with internals are examined.
Lateral forces are required in bubble columns with internals.
Presence of internals increases sensitivity of bubbly flow to lateral forces.
Internals decrease turbulent viscosity and hence enhance large-scale circulation.
Abstract In the present study, influence of interfacial forces, including drag force and lateral forces (lift force, turbulent dispersion force and wall force) on the hydrodynamics in pilot-scale bubble columns with internals is analyzed. The results indicate that the lateral forces may be optional for the hollow columns, but they are 1
required to accurately predict flow characteristics in the bubble columns with internals. Furthermore, it has been found that the bubbly flow behavior in the bubble columns with internals is more sensitive to the lateral forces in comparison with those without internals, and the complex geometry significantly alters the response of bubbly flow to the interfacial forces. In addition, despite the insignificant effect on gas holdup, the presence of internals gives rise to an enhancement of large-scale liquid circulation due to the remarkable decrease of turbulent viscosity. Key words: Bubble columns; Internals; CFD; Interfacial force; Churn-turbulent flow
Nomenclature CD
drag force coefficient
CD 0
single bubble drag force coefficient
CL
lift force coefficient
CTD
turbulent dispersion force coefficient
CW
wall force coefficient
CW 1 , CW 2 C
wall force related constant
constant in the turbulence model
dB
bubble diameter, m
dt
internals diameter, m
D
column diameter, m
Eo
Eotvos number
FD
drag force, N·m-3
FL
interface force, N·m-3
FTD turbulent dispersion force, N·m-3 FW
wall force, N·m-3
g
gravity acceleration, m ·s-2
k
turbulent kinetic energy, m2·s-2
n
internals number
nW
unit inward vector normal to the wall 2
ReB
bubble Reynolds number
P
pressure, pa
r
radial position, m
R
column radius, m
t
time, s
Tm
molecular stress, s
T Re
turbulent stress, s
u
velocity, m·s-1
UG
superficial gas velocity, m·s-1
VB
bubble volume, m3
y
distance from wall, m
z
axial height, m
Greek symbols
phase fraction
turbulent kinetic energy dissipation rate, m2·s-3
percentage of CSA
m
molecular viscosity, kg·m-1·s-1
t
turbulent viscosity, kg·m-1·s-1
density, kg·m-3
k ,
Schmidt number in the turbulence model
angular velocity, s-1
subscripts G
gas phase
i
phase
L
liquid phase
1. Introduction Heat removal is a crucial issue in the design and operation of commercial Fisher-Tropsch (F-T) synthesis slurry bubble column reactors. Dense heat-exchanging 3
tubes are equipped in the reactors to maintain the desired reaction environment. Therefore, the effects of dense tube internals on the hydrodynamics in bubble columns have gradually received attention in recent years (Al Mesfer, 2013; Bernemann et al., 1991; Besagni and Inzoli, 2016; Chen et al., 1999; Forret et al., 2003; Guan et al., 2015; Guan et al., 2014b; Jhawar and Prakash, 2014; Kagumba and Al-Dahhan, 2015; Youssef and Al-Dahhan, 2009; Youssef et al., 2013a; Youssef et al., 2013b; Youssef et al., 2012; Zhang et al., 2011; Zhang et al., 2009). Chen et al. (1999) found that the presence of internals had insignificant on gas holdup and liquid velocity profiles, but substantially reduced turbulent stress and eddy diffusivities. Forret al. (2003) reported internals intensified liquid large-scale circulation and decreased liquid fluctuation velocity and radial dispersion. Zhang (2009) observed gas holdup and liquid velocity profiles became steep in the presence of internals. Youssef and Al-Dahhan (2009) and Youssef et al. (2012) measured bubble properties in bubble columns with internals, and the results indicated that dense internals increased gas holdup and interfacial area and reduced bubble chord length and bubble velocity. Furthermore, column size combined with internals drastically effected bubble motion direction near the wall region. The measured results by Guan et al. (2014b, 2015) indicated that the internals extended the gas distributor region, and the effect was intensified in large-scale bubble columns so that the well-developed region in a 0.8 m diameter bubble column equipped with internals vanished. Kagumba and Al-Dahhan (2015) studied the effects of internals diameter on bubble properties and found that smaller size internals gave higher specifific interfacial area and lower bubble velocity. Recently, Besagni and Inzoli (2016) investigated hodlup, flow regime transition and local flow properties in an annular gap configuration bubble column, and observed that the presence of internals stablized homogeneous regime and postponed regime transition. In comparison to experimental investigation, numerical studies on the effects of internals are relatively sparse (Guan et al., 2014a; Laborde-Boutet et al., 2010; Larachi et al., 2006; Zhang et al., 2011). Larachi et al. (2006) and Laborde-Boutet et al. (2010) simulated the effects of internals in the bubble columns. The meandering 4
gas twirls were replaced by smaller pockets in the size of inter-tube gaps in the presence of internals. Moreover, higher gas holdup was observed around the tube internals. In their model, drag force was assumed as the sole interfacial force and other lateral interfacial forces (such as lift force, wall force and turbulent dispersion force) were neglected. Zhang et al. (2011) developed a 1D porous media model to simulate hydrodynamics in bubble columns with internals, and concluded that the enhancement of large-scale circulation was relevant to the decrease of turbulent viscosity. In addition, Guan et al. (2014a) employed volume of fluid (VOF) method to simulate bubble dynamics in bubble columns with internals and the simulated results showed that the bubble shape and rise velocity were significantly altered in the presence of internals. Guédon et al. (2017) employed a bi-dispersed bubble model to model an annular gas bubble column, and found that relative amount of small bubbles was important and should be provided according to empirical correlations. Recently, Bhusare et al. (2017) have simulated a bubble column with internals by Openfoam, and the predictions showed good agreement with experimental data. However, an imposed zero-void wall boundary condition was employed to force bubbles to move away from wall. As discussed by Jakobsen et al. (2005), prescribing the wall void fraction leads to an overconstrained set of equations, and should be avoided. By contrast, numerous studies focused on the simulation of hydrodynamics in bubble columns without internals (Chen et al., 2005; Jakobsen et al., 2005; Jakobsen et al., 1997; Joshi, 2001; Sokolichin et al., 2004; van Baten and Krishna, 2004). Yet consensus on whether lateral forces is required to accurately predict gas-liquid flow has not been reached. Some studies (Laborde-Boutet et al., 2010; Laborde-Boutet et al., 2009; Larachi et al., 2006; Sokolichin et al., 2004) reported that the drag force is the most important interfacial force, and the lateral forces can be neglected to give good predictions, whereas other simulations (Ekambara et al., 2008; Jakobsen et al., 1997; Krepper et al., 2005; Tabib et al., 2008) indicated that the lateral forces, such as lift force and turbulent dispersion force, are of significance to quantitively simulate bubbly flows. However, in the bubble columns with internals, the effects of interfacial forces on the hydrodynamics have not been clarified, and whether the lateral forces 5
are indispensible to predict flow characteristics remains open question. This paper is intended to target this issue. First, the governing equations and interfacial models as well as numerical strategies are thoroughly presented. Second, the effects of interfacial forces, including the drag law and other lateral forces, on the simulated results are evaluated through the CFD simulation of a pilot-scale bubble column with internals of Zhang et al. (2009). Then the mechanism underlying different hydrodynamic behaviour close to column wall and tube internal wall without considering the lateral forces is revealed, and the simulated hydrodynamics in the presence of internals is elaborated. Lastly, the related conclusions are drawn from the foregoing analysis and discussion.
2. Mathematical model 2.1 Euler-Euler governing equations The numerical simulations are based on two-fluid Euler-Euler approach. The continuity equation for each phase is ( k k ) ( k k u k ) 0 t
(1)
The momentum equation for each phase is ( k k uk ) ( k k uk u k ) k P [ k (Tkm TkRe )] Fi ,k k k g t
(2)
2.2 Interfacial forces The total interfacial forces Fi,k between the two phases are given by the drag force, lift force, turbulent dispersion force and wall force: Fi ,G Fi , L FD, L FL, L FTD, L FW , L
(3)
The drag represents the resistance experienced by bubbles passing through the liquid, including skin friction and form drag. The interfacial momentum transfer between gas and liquid due to drag is given by:
C 3 FD, L L L D uG u L (uG u L ) 4 dB
(4)
where CD is the drag coefficient taking into account of hydrodynamic interactions among bubbles, and dB is the bubble diameter. 6
The lift force comes from the net lateral effect of pressure and shear stress on the bubble surface, and is expressed as:
FL, L CLG L (uG u L ) u L
(5)
where CL is the lift force coefficient and its sign depends on the bubble diameter and bubble shape as observed by Tomiyama et al. (2002). In our simulation, the lift force coefficient is -0.02, as suggested by Tabib et al. (2008). The turbulent dispersion force is due to the liquid velocity turbulent fluctuation and is derived by Lopez de Bertodano (1992) based on the analogy with molecular thermal motion: FTD, L CTD L k L
(6)
where CTD is the turbulent dispersion force coefficient and its value is 0.3, in the range of 0.1~0.5 as recommended by Lahey et al. (1993). The wall force is proposed by Antal et al. (1991) based on the potential flow theory and is used to drive bubbles away from the wall: u uL CW G L G nW dB 2
FW , L
(7)
where CW is the wall force coefficient, and nW is the unit inward vector normal to the wall. The wall force coefficient is given as:
d CW max CW 1 CW 2 B , 0 y
(8)
where y is the distance between the bubble and wall. The wall force constants CW1 and CW2 as suggested by Ekambara et al. (2008) are -0.01 and 0.05, respectively. 2.3 Turbulence modeling The dispersed RNG k-ε turbulence model, which is recommended by Laborde-Boutet et al. (2009) to simulate gas-liquid flows, is adopted to calculate turbulent eddy viscosity:
m Lt L L k L L Lu L kL L L kL TLRe : u L L L L t k
7
(9)
m Lt L L L L Lu L L L L L C 1TLRe : u L C 2 L L L t k L R , L
C L t L
(10)
kL2
(11)
L
The related constants in the turbulence model are illustrated in detail by Laborde-Boutet et al. (2009).
3. Numerical details 3.1 Geometry The pilot-scale bubble columns with and without internals of Zhang et al. (2009) are simulated in this study. The details of geometry and operating conditions are given in Table 1. 16 steel tubes (0.025 m in diameter and 5 m in height) were installed in a 0.476 m in diameter and 5 m in height pilot-scale bubble column. The steel tubes were distributed in equilateral triangular with pitch of 0.09 m to cover about 5% of column cross sectional area. The gas was introduced into the column through a perforated plate. The perforated plate gas distributor had triangular arranged holes with 5×10-3 m in diameter and 0.06 m in pitch, which resulted in total free area of 0.61%. Local gas holdup and liquid velocity were measured in the well-developed region (axial position of 2.2 m above the gas distributor) by conductivity probe and Pavlov tube, respectively. the measured data were employed to validate the CFD model and to illustrate the effects of interfacial forces in the pilot-scale bubble columns with internals. 3.2 Mesh Gambit 2.4.6 was employed to generate hexahedral meshes for the fluid domain. The 5×10-3 m in diameter circle holes on the distributor were simplified as square holes to reduce the mesh number and computation burden. Typical grid layout for bubble columns with internals is illustrated in Fig. 1. Two layers of dense mesh were imposed near the wall to capture minimum liquid velocity point near wall and to satisfy standard wall function criterion (11.5~30
