Article pubs.acs.org/IECR
Experimental and 3D Computational Fluid Dynamics Simulation of a Cylindrical Bubble Column in the Heterogeneous Regime Marcela K. Silva,†,§ Vanessa T. Mochi,† Milton Mori,*,† and Marcos A. d’Á vila‡ †
School of Chemical Engineering, University of Campinas, Campinas, São Paulo 13083-970, Brazil School of Mechanical Engineering, University of Campinas, Campinas, São Paulo 13083-970, Brazil § Chemical Technology Department, Federal University of Maranhão, São Luís, Maranhão 65080-805, Brazil ‡
S Supporting Information *
ABSTRACT: Experimental and numerical evaluation of a cylindrical bubble column was performed in order to analyze the liquid behavior and the turbulence quantities in the heterogeneous regime of operation. Three different gas superficial velocities were tested: 3, 5, and 7 cm/s. The particle imagine velocimeter technique was employed to obtain the experimental axial liquid velocity profiles, while ANSYS 14 was used for the simulations. Velocity fluctuations, turbulent intensity, kinetic turbulent energy, and Reynolds stress tensors were obtained from the experimental data. Two drag models were compared; standard k−ε and Reynolds stress model were applied for the turbulence. Results have shown that in the heterogeneous regime an anisotropic consideration of the turbulence is more appropriate for describing the bubbly flow.
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INTRODUCTION Multiphase flow behavior is a subject of research interest both in the academic and industrial fields because this kind of flow is related to conventional industrial applications as well as emergent technologies for chemical, petrochemical, biochemical, and environmental processes. Among the equipment used for such processes, bubble columns are widely employed because they can promote high mass and heat transfer while having relatively low operational costs. In bubble columns, gas holdup, turbulence, bubble size distribution, and how the phases interact with each other are related in a complex way with the project and operation variables. Thus, a deep knowledge about its fluid dynamics is necessary.1 Therefore, the use of appropriate tools for developing scale-up strategies and flow pattern comprehension is very important. During the past decade, the number of contributions in which computational fluid dynamics (CFD) is applied increased considerably. With this technique it is possible to represent the flow behavior in a bubble column investigating the influence of the operational parameters. In spite of the increasing number of the CFD studies in bubble columns during the last century, they still have some limitations on modeling how the phases interact with each other. This occurs because of the lack of experimental data for the heterogeneous operational regime for testing the applicability of models used in the simulations. Even with advances in measurement techniques, there are few works in the literature dealing with experimental data for gas superficial velocities corresponding to the heterogeneous regime.2−4 In this context, this work presents an experimental and numerical study of a bubble column operating in the heterogeneous regime. Particle imagine velocimeter (PIV) was used for the measurements; velocity fluctuation (RMS), turbulent intensity, kinetic turbulent energy, and Reynolds © 2014 American Chemical Society
stress tensor were calculated from them. Then, the axial liquid velocity profiles were compared with the model applied in a previous work5 to describe the liquid behavior. Results have shown that for a bubble column that operates in the heterogeneous regime it is more appropriate to consider an anisotropic approach for turbulence.
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MATHEMATICAL MODELING In this study an Eulerian−Eulerian approach was employed to describe bubbly flows. The model equations are presented in Table 1, where ρ is the density, α the volume fraction, u the velocity vector, μ the viscosity, p the system pressure, and g the gravity acceleration; Mcd are the momentum transfer rate between the phases, and Tt is the Reynolds stress. The subscript k indicates the phase: c for the continuous phase (liquid) and d for the dispersed one (gas). In eq 1, the source therm is zero because no mass transfer is considered. The interfacial forces of lift, turbulent dispersion, and virtual mass were neglected. According to the previous work of Silva et al.5, only drag force was considered for the evaluated study cases. Turbulence was modeled using Reynolds averaged Navier− Stokes (RANS) equations, where the instantaneous variables in the momentum equation (eq 2) are defined as the sum of an average value and its fluctuation. The term Tt = ρu′ku′k in the total stress tensor is known as Reynolds stress and represents the turbulence effects and is added in the momentum equation. Different methods are found in the literature for the modeling of Tt. In this study two approaches were employed: the Boussinesq hypothesis and another in which a transport equation for each stress tensor is employed. When the Received: Revised: Accepted: Published: 3353
September 12, 2013 January 3, 2014 January 31, 2014 January 31, 2014 dx.doi.org/10.1021/ie4030159 | Ind. Eng. Chem. Res. 2014, 53, 3353−3362
Industrial & Engineering Chemistry Research
Article
Table 1. Summary of the Governing and Constitutive Equations Governing Equations: Mass and Momentum Conservation
∂ (ρ αk) + ∇·(ρk αk uk) = 0 ∂t k
(1)
∂ (ρ αk uk) + ∇·(ρk αk ukuk) = −∇·(αk T) − αk∇p + αkρk g + Mcd ∂t k Constitutive Equations
⎛ ⎞ 2 strain stress: Tk = αkμk ⎜∇uk + (∇uk)T − (∇·uk)I ⎟ + αk Tt ⎝ ⎠ 3
momentum exchange: Mcd =
McdD
(2)
(3)
(4)
C drag: McdD = D Acd ρc (ud − uc)|ud − uc| (5) 8 Turbulence Equations k−ε: μt = Cμρk
k2 ε
(6)
⎡⎛ μ⎞ ⎤ ∂ (ρk αkkk) + ∇·(ρk αk ukkk) = ∇·⎢⎜μk + t ⎟∇k ⎥ + Pk − αkρk ε ⎢ ∂t σk ⎠ ⎥⎦ ⎣⎝
(7)
⎡⎛ μ⎞ ⎤ ε ∂ (ρ αkεk) + ∇·(ρk αk ukε) = ∇·⎢⎜μk + t ⎟∇ε⎥ + k (Cε1Pk − Cε2αkρk ε) ⎢⎣⎝ ∂t k σε ⎠ ⎥⎦ kk
RSM: k =
1 u′ku′k 2
(8)
(9)
∂ (ρ αk uuk) + ∇·(ρk αkuk uuk) ∂t k ⎞ 2 ⎛⎛ k2 ⎞ 2 = γ + ϕ + ∇·⎜⎜⎜μk + csρk k ⎟∇uuk⎟⎟ − δαkρk εk εk ⎠ 3 3 ⎠ ⎝⎝
(10)
⎛ ⎛ μ ⎞⎞ ε ∂ (ρ αkεk) + ∇·(ρk αk ukεk) = ∇·⎜⎜αk∇ε⎜μk + t ⎟⎟⎟ + αk k (cε1γ − cε2ρε) ∂t k σ k ⎝ ⎠ ⎝ ε ⎠ k T
γ = − ρk (uuk(∇uk) + (∇uk)uuk)
(11)
(12)
Population Balance Equations
∂ (ρ αdf ) + ∇(uiρi αdfi ) = BBi − DBi + BCi − DCi ∂t i i breakup birth rate: BBi = ρd αd(∑ G(vj ; vi)fi )
(14)
j>i
breakup death rate: DBi = ρd αd(fi
∑ G(vi ; vj)) j
